Randbats is not a tier by definition. It isn't part of Smogon's tiering system, which only includes Ubers, OU, UU, RU, NU (and the BLs in-between). Everything else is just referred to as a metagame or format. Randbats is most certainly a metagame, regardless of what you think of it.
As for whether Randbats is competitive or not, I would say that it is. There's enough variety in the teams for it to be balanced majority of the time. There's a very low chance of getting a poor team match-up (i.e. team with four Water-types against a team with three Electric-types) that you can do absolutely nothing about; usually there's something you can do to turn things into your favor. But sometimes that isn't always the case. However, if one were to argue that Randbats aren't competitive because they're occasionally too reliant on match-ups, then I could also argue that metagames like BW OU shouldn't be considered competitive either. BW OU battles are often decided by team match-ups (i.e. sand offense beats rain offense, sand stall beats rain stall, etc. and there's little to nothing you can do about it). Additionally, Randbats rarely gives any Pokemon that aren't usable at all; sometimes they can be used if you save them for later, sometimes they can be used as death fodder. Point being, Randbats is hardly any more team match-up reliant than some of the other more serious metagames. I will also add that Randbats has less of a surprise factor than any other metagame that allows custom teams, because Pokemon generally have set movesets that they will always have (occasionally with a different item or move). (There's even a list of them on Smogon, but I can't be bothered to find it.) Meaning, you can usually predict what the opponent can and cannot do from the start of the battle. It's similar to chess in a way, in that you know everything that each piece can do so there's not quite as much luck involved. You don't have deal with the ridiculous amount of versatility that a lot of Pokemon have in the newer generations.
One thing I like about Randbats (particularly in regards to playing in smaller battling communities like PC) is that each battle has different teams. So, you can battle the same person over and over without them knowing your previous team. This makes battling against the same group of people much more enjoyable, because you don't have to worry about your lures no longer having a surprise factor and all that jazz. Not having to make any teams is an obvious convenience too.
However, I find that Randbats 1v1 tends to be even more dependent on team match-ups and luck. Some Pokemon simply aren't cut out to be usable in 1vs1; they generally need to have a lot of coverage moves and a small amount of weaknesses. This means that stuff like Chansey that would otherwise be useful in a 6v6 match will be taking up your available options. Oftentimes I feel like I can't do anything at all to win in certain 1v1 matches because I don't have enough Pokemon that are actually usable those types of battles.
But you know what isn't competitive at all? Challenge Cup.
