No. UA is offering upgrades to the next class of service on selected international flights (mostly inbound to the US), but that appears to be happening only at the gate.

Also, by day of flight, the only elligible fare class would be Y, though a Y fare can have it's advantages depending on your needs (I myself buy Y for my annual SEA-NRT flight since it offers me a ton of benefits that make it worth twice the price of the minimum H fare).