Programs: UA 1K MM, Hertz PC, BAEC Silver, Glob Entry
Technically it was not possible at all until earlier (the start?) of this year - the line was for Premium Economy (on some airlines), Business and First only. Then for a short period, UA paid to allow others through - whether it was 1K or E+, I'm not sure but I was specifically told at check in that this was now possible.
Then, either on or shortly after 3/3, UA stopped paying and I was specifically told at check in that the priority line was no longer available due to cost cutting by UA.
Now, to the non-technically bit. The line is, of course, operated by BAA, not UA, and the old gold boarding card stock fooled quite a few of the bp checkers into thinking that this was a premium class product - so they let people through. This can still happen but IME never when I haven't been issued a gold bp. So, YMMV but I wouldn't count on it. Having said that, even in the normal line it has never taken me more than ten minutes to get through - usually a lot less.
I think officially it's only for C and F passengers. Try as a 1K if you like. I sometimes get through but I have also been redirected to the regular line. Also depends on loading, sometimes regular lines are shorter if they have all lanes open.