It won't get you a elite status, just a status slightly better than the normal flyer -- and free tickets too.The lowest tier on the major US carriers is 25k qualifying miles/year. So to maintain the lowest-level status on two of them requires 50k miles/year, and to maintain that on all three requires 75k/year (and remember these are qualifying miles -- you can't get them from pudding cups or other promotions, and while there are ways to get more qualifying miles than you've flown, you either have to actually put your butt on a plane or spend a lot of money on a credit card).
Coincidentally, 50k is the next tier up on all three airlines, and 75k is the third tier up on two of the three (American is the odd one out, with only three tiers instead of the four at Delta and United). And to be frank, the "benefits" of the lowest tiers on all three are garbage. You might, if you're lucky, score an extra-legroom seat a few times a year on Delta, for example, or maybe once or twice get an upgrade on a domestic flight (but only if it's not on a busy route).
So if you're going to fly enough, you really should aim to get worthwhile status on one airline before spreading miles around to others.
(I'm currently Executive Platinum on AA and Platinum on DL, and know whereof I speak on the worthlessness of the lower tiers, since I've had to put up with them in the past)