What does "upgrade with cash" mean? Do you mean paying the fare difference to get into first class (whether actual F or a discounted first class fare bucket), which isn't technically an upgrade? Yes, that is not possible, since the companion ticket is only for coach fares. But once purchased, they are regular coach fares like any other, earning miles and eligible for upgrades with instruments or elite status complimentary upgrades into U like the underlying, non-discounted cash fare. The only stipulations are that the companion can't travel without the primary passenger and that they can't be changed to paid first class (discounted or F) fares.

I edited the wiki to clarify that it's first class upgrade (U) space, not F space, that needs to be available. If I have the upgrade space inventory code wrong, someone please correct!