Yes, but it's almost always cheaper to cancel your ticket and rebook the cabin you want.
For example, my RAK-EWR flight yesterday was booked for 28K miles in coach. PremEco was 55K and Polaris was 80K. Upon check-in (and leading up to), UA wanted 39K miles to upgrade to PremEco and 199K to upgrade to Polaris. Those would have been in addition to the 28K I already spent. The flights were still going for 55k/80K up until flight time if booked as a new ticket.
-RM