If your training heavy snatches is it necessary to do any other pressing? I can’t think what muscles would be trained by a press that aren’t trained by the 3 TSC lifts given the snatches are heavy enough.
A strong press does let you snatch heavier, which means test bell becomes that much lighter, so more reps = better performance in TSC. So working on the press is still necessary in a year-round plan with twice a year TSC training, just maybe not as much in the 6-8 weeks leading up to each one.
I think a lot of people who train seriously for the TSC do little-to-no pressing. There is already a lot of overhead work with pull ups and snatches, so many people find that to be sufficient. So is it "necessary" ... probably not. Could you do it if you wanted to? Probably
@Simply strong IMO, a light/moderate weight for warmup, or if you have a variety of bells, work up a ladder to a moderately heavy bell, perhaps even a partial rep with a bell you can’t yet do a full rep with.