AFAIK yes, but there should also be a line in your PNR showing the upgraded class (it won't say confirmed or let you choose a seat) as well as the line showing you confirmed in coach on the same flight. It might look at first like you can select a premium cabin seat, but don't get excited as this doesn't mean that you've been upgraded and you won't be able to pick the seat. When the wait list clears, you will see some message to contact DL.

There have been various opinions here regarding whether the wait listed flight line should be above or below the line for the same flight confirmed in coach on your PNR.

Often I'll call the following day and nicely ask an agent to look at the ticket and PNR carefully to check that everything has been done correctly with the SWU.

When the wait list clears and you call, the ticket will either be reissued immediately (new ticket number and new email receipt) or it will go into the reissue queue. For confirmed upgrade space on partners, I always like to see the ticket reissued right away to avoid risking that the upgrade seat will be lost.