It won't add much if you pick an appropriate tunnel server.

All my packets go through Seattle, using a Seattle tunnel server adds negligble latency.

But as someone else said, being connected with an he.net tunnel gets you marked as undesirable traffic these days, so that's annoying.

HE has a lot of points of presence in North America and Europe: https://pop.he.net/ , so latency should be negligible there. Elsewhere, yes you might see higher latency.

Possibly. They let you pick your nearest server, and HE is a tier-1 ISP which a lot of your packets may traverse already.