I don't think so. Just like now, to be counted as a team you just have to have an arenateam. That team is counted towards the whole pool of teams which is counted towards what amount of teams are getting titles.
To be eligible for the rewards, you have to have 20% played, within 100 rating and withing certain % of all teams to recieve a title.
So you could, just like right now, make as many arenateams on your shitty alts to increase the amount of titles that are given out. And if there's no arena teams next patch, you probably don't even have to play any arenas to be counted in the pool of players or have to play one arenagame, depending on how they implement the system technically.
No. A ranked
team is one that has 20 games played and at least one eligible player in it. All other teams are not ranked, they are not included or counted in the rankings in any way at all.
There's ~40k ranked teams on EU (I summed all the bottom ranks of all BGs). If we say that on average, there's 3 players per team, that's ~120k players; this is a guesstimate of course, there's no good method to determine average players per team. That's 600 Gladiator spots and 120 "rank 1" spots, and this is a pretty modest estimate.
A lot of casual or "non-serious" characters don't keep their teams, they leave the ranking system completely every time they do this. In the new system, it's not possible to leave the ranking system. Once you played 50 games, you're in the system till the next season. That's a huge amount of players.
On top of that, I believe arena in general will be more active now than before due to crossrealm queuing and novelty of the system.
I'd say 1k+ Gladiator spots and 200+ "rank 1" is very well possible for S14.