To complete the national dex, you won't need mythical Pokemon who require events to obtain normally, so yes you can still complete the dex. You will, however, need to be able to transfer, at the very least, from gen 4 games (DPPt & HGSS) which will also require a second DS. If you wanted to make it easier to catch gen 3 Pokemon you would need a DS that can play GBA games to send them to your gen 4 games and then to gen 5.
These Pokemon are not catchable in gen 5.
If you wanted mythical Pokemon anyway, you can follow the instructions in this video.