Not exactly.
It depends on if you want a top safety lever or not. Without modifying the tang of your 722, a 700 top safety trigger will not work. A 700 short action stock will work fine, but you either have to put on a 700 trigger and make a cut on the the tang of the 722 action or inlet the 700 stock for your 722 trigger safety lever. On a 722, it has a full tang and the lever sweeps on the outside. With a 700, the tang has a cut-out on the side for the safety lever to ride closer to the action.
Can't swap the 722 lever over to the 700 trigger either because the construction on the lever where the ball rides into it's hole on the trigger housing is slightly different from a 700. With my custom 722, I used a 700 short action stock, 700 short action BDL bottom metal, and used a Jewell 700 trigger with the bottom safety so I did not have to make mods to the stock or tang of my action. They also make 700 triggers without a safety. Another option is to just remove the safety lever from your 722 trigger. Safety levers may not be an issue to some folks if it is a varmint rifle that will only have a round chambered right before firing, but it is still highly recommended to have a safety IMO.
You will also have to get a new magazine either way if planning on using a 700 stock unless you go with an ADL model stock. The 722 magazine is the same as an ADL with the longer sloping bottom that will not work in a BDL stock.