Player A joins the ''player search que", 45 secs later Player B joins the Que....and within 2-5 secs they find each other. Is that doable?
Yes, it is doable, if you have enough players.
As hplus0603 points out, its all about the probability that another player actually will join within 45 seconds.
With too few players, that probability is too low, so most of the time another player will not join the queue within time.
Others can probaby give you a more accurate calculation, but if you consider that in 8 hours you have 640 "45 s slots", it should be pretty easy to see that distributing 1000 players randomly among those 640 buckets will have a high probability of players being alone in their bucket.
Now the players aren't perfectly randomly distributed, there are highs and lows, but that just makes the problem worse in the lows.
(the bucket approach is a pessimistic estimate, since two players in neighbouring buckets might be within 45s of each other, but I think it still is useful to understand the scale)