In a qualified manner, yes. In an unqualified manner, probably, I need to find more specific sources.

Let me unpack that a little.

Satsuma Domain, under the Shimazu, had a complex relationship with what is now called Okinawa and was then known as Ryukyu. In 1609, they launched a "punitive" expedition in which they essentially conquered the islands, forcing the king to travel with them back to Japan, meet with Ieyasu, and formally submit as a vassal to the Satsuma domain.

However, the islands weren't just absorbed entirely into the domain. The king was returned to the island and was allowed to take the throne again, and in fact some effort was made to hide his new vassal relationship from representatives of China, to whom Ryukyu also sent tribute. The Shogunate was eager to maintain a conduit for trade with China through the Ryukyus, and didn't want to endanger that by disrupting the islands' relationship with China.

This meant that, even after the seemingly iron-clad ban on overseas travel, Satsuma was regularly sending ships to the "independent Kingdom" of the Ryukyus, conducting trade not just with the islands themselves but also from there to China. Even after Chinese trade began passing in volume through Nagasaki, Satsuma continued its trade with Ryukyu.

The other main avenue for foreign voyages was through the Sou clan, daimyo of Tsushima. They had been conducting trade with Korea since well before the Edo period, and were the official link between the Shogunate and Korea throughout the reign of the Tokugawa.

Korea's relationship with Japan was somewhat unique in that it was an official contact between states, conducted as if between equals. The Sou clan acted essentially as the Shogunate's ambassador, and operated a Japanese-held concession in Busan on the Korean peninsula known as a wakan/waegwan/倭館, a Japanese hall or house, though in actuality it was more like a small settlement or district. This had permanent Japanese residents and functioned both as a local site for diplomacy and a trading post for the exchange of goods -- notably silver and copper on the Japanese side.

What I need to find more specific sources on is where the ships actually physically carrying these goods came from -- were they built on Tsushima, did they have Tsushima domain crews, etc. If anyone more familiar with the relationship between Korea and the Tokugawa Shogunate can chime in, please do. Otherwise, I'll make a follow-up edit if I can get access to better sources on seafaring and maritime trade in Tsushima.

So, in summary, yes: ships were leaving Japanese ports bound for foreign shores. Sakoku (a term which wasn't even really in use in the 1600s in Japan to the best of my knowledge) is somewhat overblown in terms of the "absolute isolation of Japan." Plenty of trade was happening, to the degree that the Shogunate actually became concerned about the volume of silver and copper leaving the country in exchange for foreign goods. Ideas and information were coming into the country from China and Korea, and of course famously from the Dutch -- so called "Dutch learning"/蘭学. Of course, not all the books were written by the Dutch, some were from elsewhere in Europe and merely translated into Dutch. To some degree it was less "a country in chains" and more "a country in a sweater" with several planned, comfy openings.

Sources:

Sakai, Robert K. “The Satsuma-Ryukyu Trade and the Tokugawa Seclusion Policy.” The Journal of Asian Studies, vol. 23, no. 3, 1964, pp. 391–403. JSTOR, www.jstor.org/stable/2050758. Accessed 13 Mar. 2021.

Kazui, Tashiro, and Susan Downing Videen. “Foreign Relations during the Edo Period: Sakoku Reexamined.” Journal of Japanese Studies, vol. 8, no. 2, 1982, pp. 283–306. JSTOR, www.jstor.org/stable/132341. Accessed 13 Mar. 2021.