Well the cup would still have everyone participate. Only that there would be a lot less bot teams in it.
As long as there were never more than 4096 active teams when the Cup draw is begun, no VI series would be required - that's the highest power of two that fits within the 5456 teams available in levels 1 through 5 combined. (1 + 4 + 16 + 64 + 256 = 341 total leagues, times 16 teams per league). I don't know if any nations were ever above that point in the past, though I do know Italia and Espana are within roughly 10% of that right now. But I also think they've said that the bot level games may not be simulated as in-depth and I am certain from looking over rosters in that level that they don't have training/GS updates.
Basically, though, the whole bot leagues thing as factors into server resources is an irrelevant argument either way. The appeal of private league games is that they occur on days where games are not normally occurring, so whether they had to simulate worthless bot games or not doesn't change the amount of server resources available on a current non-game day. The thing that would determine whether resources exist are what other processes might be running on those days - like economic updates on Monday. My best guess is even if there is some sort of maintenance going on each of those days, there probably is an avenue to open up for second PL games on one of those days, even if it's in a more limited window of times as compared to the times allowed for Friday and I think that definitely would be something that BB should definitely seriously consider - whether it just be a second PL or some sort of international supporter-only competition.