A bike made of 2.5 mm thick steel would be heavy, but as long as your joints are sound there's no reason you can't build a bike. You should make a joint and then cut it in half from time to time, and look at it really carefully to make sure you've penetrated sufficiently and that the bits you thought were welded really are.
Check out Atomic Zombie's books on building your own bikes of various designs from scrap frames etc. Mostly they suggest welding, as MIG welding is relatively easy to learn, and cheap to do once you own the machine. It's quite hard to make really neat welds in thin-walled round tubing, though - that's usually done in production with a TIG welding machine which is a new level of skill and expense.
If you want to build elegant machines from thinner-walled steel tubes, I'd suggest learning to braze. You'll need a small oxyacetylene rig for that, but the results are just as strong, much nicer to look at and you can build much lighter bikes.
And to answer your original question, no I haven't built a bike from scratch. But I've made substantial modifications to several which are still in one piece and haven't broken! And I make custom racks for recumbents and Moultons from time to time, all fillet brazed in mild or 4130 cro-moly steel.