And are there any archaeological data about silk in pre-Imperial Rome?
Silk, being a fragile fabric, is going to be lost in virtually any archaeological context.
THIS article says:
SE′RICUM (σερικόν), silk, also called bombycinum. The first ancient author who affords any evidence respecting the use of silk, is Aristotle (H.A. V.19).a After a description, partially correct, of the metamorphoses of the silkworm (bombyx, Martial, VIII.33), he intimates that the produce of the cocoons was wound upon bobbins by women for the purpose of being woven, and that Pamphile, daughter of Plates, was said to have first woven silk in Cos. This statement authorizes the conclusion, that raw silk was brought from the interior of Asia and manufactured in Cos as early as the fourth century B.C.
A footnote then says that a recent historian pushes this back another hundred years or so.
Silk is fragile and most silk objects do not last very long.
However, the coronation mantle of the Holy Roman Empire, woven in Palermo in 1133/34, is preserved in Vienna aged about 884 years and as far as I know was last worn in 1792 when aged about 658 years.
And there are many much older silk fabrics in museums.
In 2006, Archaeologists in Rome uncovered items in wooden boxes which may have been imperial regalia - spears, bases for standards, scepters, etc, which were wrapped in "linen and what appears to be silk", believed to have been buried after the defeat of Maxentius at the Milvian bridge in 312 AD. If "what appears to be silk" actually is silk, and the date is correct, that is archaeological evidence of silk in the Roman Empire a mere 339 years after the usually accepted starting date of the Roman Empire in 27 BC.
So far that is the closest I can get to "archaeological data about silk in pre-Imperial Rome".