In terms of strategic morale (as well as tactically saving a cadre that could be used and redeployed elsewhere), it was very important. Heavy equipment (that was lost) is expensive, and you don't want to abandon it if at all possible, but trained and combat experienced manpower is also extremely valuable, and saving over 300,000 troops that might otherwise be lost to future efforts is nothing to scoff at.

The second part of your question is a bit ambiguous? Do you mean, "Would the UK have been forced to surrender if the withdrawal had been a failure?"

If that was your intended question, then the answer is "No, not at all." Losing those soldiers would've been a significant blow, but the British did not escape France unscathed as it was. The BEF lost almost 70,000 men in France as it was (and lost other formations wholesale that were cut off to the south) and remember of the "army" that was extracted, they'd lost all of their heavy equipment, tanks, plus significant tonnages of ammunition and stores. In other arms, the Royal Navy lost six destroyers, a number of other ships, and the RAF didn't get off scot-free either. So this wasn't exactly a stunning victory in any case.

But being kicked off the continent is a far different scenario than being forced into a surrender.

Remember, there's a very strong argument to be made that Operation Sealion (the follow-up proposed invasion of England) was flawed and basically unachievable regardless of whether the aerial Battle of Britain was decisive or not - the argument has been made that the Kreigsmarine lacked the capability to launch a viable amphibious assault on the British Isles... There's really no reason why Britain would have been forced to surrender (and wouldn't have) if Operation Dynamo failed.