In the present states like UAE, Bahrain and Saudi Arabia, were there more nomadic people than sedentary or settled Arab peoples during the 7th century?
There was much more settled population than nomadic one. Also, there was more Arab population than Bedouin.
First, the Arabian peninsula has only one population center, the Hijaz, which is barely suitable for agriculture, and somewhat suitable for heat-resistant animal grazing, such as camels, goats, and donkeys. This area runs along the Red Sea coast and has better lands in the south (present-day Yemen).
Second, the Persian gulf is a poor sea, since it has not enough oxygen, nor receives enough freshwater with good sediments with nutrients. It has barely any fish or mollusks to collect. On the other hand, the Red Sea is much better, although it does not have any good fishery like the Atlantic ocean. On the contrary, the Indian Ocean is quite good.
That said, the Peninsula has never had a strong population. Even during the late Roman Empire, it was largely ruled from cities in the north "Arabia Petraea"=the rocky Arabia in the fringe of the desert, in south Syria and Levant. The center of the peninsula was not even under any government or province, guess why! It was named "Arabia Deserta". The south, including Oman, Yemen, was named "Arabia Felix = The Happy Arabia", and it had the bulk of the population of the whole peninsula, in coastal settlements and in the Hijaz.
In addition, in 7th century, most of the trade routes to Asia did not pass through Arabia, but rather Mesopotamia and Syria. Arabia had some good trade routes to Africa. So, there was really little population in present day UAE, Bahrain and also in Saudi Arabia too (excluding the mentioned Hijaz and the northern part near Ancient South Syria/Today Jordan).
That said, nomadic population density is always much, much lower than settled-agricultural people. The difference is like 20x. Nomadic people can also become settled for some months each year, and they can also live in towns and cities they travel to for several years. So, often there is no clear distinction, as it was the case in Arabia in the 7th century.
So, there was much more settled population that nomadic one. There was more Arab population (hadir) than Bedouin. Also, many culturally Bedouin were setteled people, just as today. Consider the Arab population average man to be like a Yemeni goatherd rather than a present-day, Saudi Arab rich merchant in Mekka.
For population numbers, I've never seen historic figures from the 7th century, but have in mind that during the XX century population has changed a lot in the Arabian Peninsula. The UAE did not have 100k people in the 1900, much less in 7th century, but now they're nearly 10 million. Same evolution for Bahrain and Saudi Arabia.