Can a deal still close if one condition hasn't technically been satisfied yet?

Yes, if the party the condition was meant to protect agrees to waive it or accept an undertaking that it will be satisfied shortly. Most conditions in a purchase agreement exist for one side's benefit specifically — a financing condition protects the buyer, for instance — and that party generally has the right to waive its own condition and proceed without it, even though the condition itself was never technically met.

Whether waiving makes sense is a separate question from whether it's legally possible. Some conditions protect against a real, ongoing risk, and giving them up to keep the closing date can mean losing leverage or a later remedy tied to that unmet condition. Before agreeing to close on that basis, it's worth understanding exactly what you'd be giving up — some purchase agreements treat closing without objection as accepting the situation as-is, which can affect a later indemnity claim over the same issue. A quick conversation with your lawyer about what waiver actually costs you is worth having before the closing proceeds.