Your DNA data will stay on the gedmatch website, you can get to it by logging in to that site. You won't get people added to your tree automatically but when you connect to other families in the tree you'll hopefully link to people who have tested and uploaded to gedmatch, then you can do a one-to-one gedmatch comparison straight from the Wikitree page and formally confirm the relationship between you. Fleshing out your tree by adding your ancestors' siblings is a good start.
On Gedmatch you can also find Wikitree cousins by checking your 'One To Many' results for anyone who has a link that says 'Wiki' - that shows that they've linked their Wikitree profile to Gedmatch. The link goes to their compact tree view, and the 'Gen' column shows approx how many generations up your shared ancestor should be.