Yes, it's quite possible to create all of the species without using the VST, cheats, or exploits of any kind. You really don't need to keep all that many seeds to do it, either. If you have a handful of critical seeds, and focus on one "group" at a time, it's pretty straightforward.

Where people get into trouble is doing random breeding and trying to save all the intermediate seeds. You can create any Tier 1, 2, or 3 plant from just the critical 4 Tier 1 starter seeds. If you have the right 2 Tier 4 seeds in addition to those, you can make any of the species in the entire game with just a few cross-pollinations.