In at least a few cases, yes. Some of Europe's forests, both temperate and coniferous, experienced severe strains during the 17th and 18th c. due to naval construction. (The demands of metallurgy, which required processing wood into charcoal, being the other major industrial usage.)
Among the natural resources needed for the construction of sailing ships, two came directly from forests. The timbers making up the ships' hulls took up vast quantities of oak. This could be sourced from England, Germany, France, Italy, and the eastern Mediterranean. All suffered major deforestation. Firs were needed for masts, and pine or spruce for spars and yard-arms, and could come from either Russia, the Baltic, the Pyrenees, the Alps, or the New World. As with the other sources mentioned just above, these too suffered serious depletion from naval use. Two more major materials were secondary products of the forests: tar, derived from naturally occurring resins in the trees, and iron, whose production required first turning enormous quantities of wood into charcoal for the smelting process.
The latter was responsible to a significant degree for the exhaustion of Norwegian forests by the mid-1600's. Denmark-Norway had long been a prime source both for masts and timbers for Spain, England, the United Provinces and the Hanseatic city-states. But over the course of the 17th c. a growing share of Norway's wood resources were directed to smelting, and Norwegian forests basically suffered a collapse by the 1670's which took decades to recover from. (The slack was quickly taken up by forests further east, in Sweden, Russia, and Poland, the latter two areas duly suffering their own forest exhaustions by the late 18th c.)
Elsewhere, major forest crises occurred in virtually all regions of France--most notably in Languedoc, Provence, Auvergne and Burgundy, which were heavily exploited for oak trees, and in the Pyrenees, which were used (with only mixed success) as a source of wood for ship masts. France, like every other power, used to source its timbers and naval stores from the Baltic, but this began to change somewhat at the accession of Louis XIV. Before large-scale domestic exploitation of French forests could begin, an inventory of the resources at-hand was undertaken in July 1661 at the instigation of Colbert, Louis' controller-general (French equivalent to a finance minister). Colbert was actuated partly by the prevailing economic theory of the time, mercantilism, which called for high tariffs to promote domestic industries (lumbering, in this case) from foreign competition and keep precious gold from flowing out to pay for imports; and partly because in a broader sense he viewed the chaotic governance of the French kingdom, with its decentralized administration and morass of age-old customs and regional privileges that often led to forest exhaustion, as a threat to the powerful state which he sought to build up. The 1661 statute was intended to centralize the administration of France's forest and give the navy a sustainable source of domestic timber and masts. The details are intricate, but in broad strokes, Colbert sought to impose strict controls on the cutting down of forests, which had occurred at an alarming rate to make way for agriculture and to feed new industry.
Unfortunately, both for the environment and for the French navy, the law wasn't terribly effective. For one thing, in classic French fashion, it was often ignored, so deforestation continued apace. Furthermore, it was useless in many parts of the country since canals and rivers were the only practical means of transporting large, heavy pieces of lumber, and they didn't always flow near the forests. And most concerning, from the navy's perspective, was the quality of domestic forests, which in the opinion of France's own naval architects weren't capable of producing wood on nearly the same plane [hehe] as that sourced from the Baltic. No carpentry expert I, but it seems that the climate of Northern Europe and the tall, dense forests, yielded trees with an even grain and few knots or kinks. Trees from the Pyrenees weren't as good; and the best ones had been cut down anyway. By the 1700's, the French also found that their sources of oak were dangerously depleted; it turns out that the best oak trees for shipbuilding were between 100-200 years old, and deforestation meant that few of these grew in areas which allowed for economically viable transport to the major dockyards.
All of this took place in the context of what has to be the most-active century of sustained naval warfare in human history (1670's - 1815); Great Britain made some use of the forests of its North American colonies, but for everyone else, and particularly the French, the only options were domestic (mediocre quality, and severely depleted), parts of the Mediterranean including Italy and the Balkans (ditto, plus far away), or the Baltic (all of the above, plus subject to British interdiction). Wartime emergencies (1744-48, 1755-63, and 1778-83) drove ghastly forest-cutting efforts in France, with the navy only picking out the scant bits that were suitable for shipbuilding and letting the rest rot away. Europe's forests only recovered gradually in the century after 1815.
Bamford, Paul Walden. Forests and French Seapower, 1600-1789. Toronto: Toronto UP, 1956.
Pourchasse, Pierrick. "Les Munitions navales du nord: Produits et circuits d'approvisionnement". In Les marines de la guerre d'independance americaine (1763-1783) - L'operationnel, Chaline, Olivier, Bonnichon, Philippe & Charles-Philippe de Vergennes, eds. Paris: Sorbonne UP, 2013.