Generally, yes. But the key issue is whether or not the ticket is actually issued. There is a two step process that isn't always visible to the customer...booking and paying, then the airline issues the ticket. There have been reports that there have been problems when a cruise line doesn't pay within the expected time, that the airline doesn't issue the ticket, and the customer is in for a surprise.
I would go to the United website, and where it says My Trips, enter your last name and your 6 character Record Number (something like BQ2FTW). If a flight shows up with the correct info, you may get some options, like getting a confirming e mail, or other things that will reassure you.