Yes, United Airlines offers paid upgrade (not at check in counters/same day like AS though). You usually get the offer 1) after your purcahse your ticket, an offer will pop up asking you to buy right away. 2)when using online easy-check in you will be asked if there are seats available. 3)when checking in at the airport using automated check in machines. 4)when in at regular counters and agent will ask you.

The price is more expensive than AS though. UA charges about $65 per 500 miles of distance where as AS charges $50 and tops off at $250 I believe.