You probably should have asked in the romance forum, but YES, you can and should do BOTH at the same time.
The Golden Heart is a fabulous "cred" for an unpublished writer. (I've got a final in the Golden Heart myself.) So, you can still submit the thing even if it's entered in the contest. You just can't have sold it before the entry.
Besides, you don't grant rights to the agent. You only grant rights to a publisher. So basically what they're saying is, you can't have sold this ms before the entry deadline.
Even if you get an agent before the contest is over, if you final in the GH, that's still a good solid cred an agent can use to push your work.
Plus, there have been sales because of Golden Heart finaling. We have a new Super author who was bought a couple of months ago because one of the Super editors read her ms in the final round of GH judging, and bought it. (She didn't WIN the GH, but finaling got her SOLD.
)
So, go for it!
Susan G., Golden Heart Finalist Class of 2002.
PS - I sold a different ms between the entry deadling and announcement of GH finalists. My editors bought my GH ms the day before the GH/Rita ceremony -- which happens a few times a year, that a finalist sells their GH finalist ms at the conference.