Yes, a well patched tube will hold air just as well as a new one.

IME preparation is more important than the specific patch kit brand. You've got to get the mold release off the tube before anything will stick to it, so use your grater or sandpaper to get all the "shiny" off around the patch. I've used Rema glue in the patch, but now I'm using Slime from the auto parts store, and I haven't seen a difference. Had to ask for another box of 100 Rema patches for Christmas last year, I finally used up the first box.

Glued-on patches, I usually have something go wrong (like a blow-out, long cut, or the stem starts leaking) before I accumulate more than a dozen or so patches. That's probably over five years of service (I don't label tubes!). Glueless patches usually last me 2-3 years before they start to leak.

I usually accumulate a half dozen leaking tubes (replacing them on the road) and patch them on a rainy weekend. Sand one, put the glue on, sand the next and put the glue on that, go back and put the patch on the first, and continue. I'll do an overnight leak test the next day. Oh, one more tip: get yourself a sliver Sharpie to mark the hole, especially if it's a small leak you need to find in a sink full of water.