Without the box, the only way to know if the gun you are looking at is subject to the recall is to contact Smith & Wesson. If it is within the known recall serial number range, they'll want to examine it. The risk if you send it to the factory is that if the gun in question fails the test, they won't return it.
In my opinion, there is no risk to a user of a Model 624 subject to the recall so long as the ammunition used is factory .44 Special ammo, and if handloads are used, care must be taken not to load exceedingly hot rounds.
Also, if the original factory combat grips are missing, that is a big negative as far as value is concerned. A replacement set of factory combats can run $250 to $300, depending on color and grain pattern.
Good luck in your evaluation of the gun. It is one of S&W's finest creations.