How do You figure it shall work ?
The 737 FCOM/QRH doesn't say what minimum speed should be attained during stall recovery at high altitude before attempting to return to level flight.
However, a handy guide to what minimum IAS you should attain before levelling out after a stall recovery process lies in the Boeing 737 Classic FCTM under Chapter 4 - Climb, Cruise, Descent, Holding. Sub heading: Holding Airspeeds Not Available from the FMC. It states among other information: Above FL250, use VREF40 +100 knots to provide adequate buffet margin.
Depending on actual weight of course, then for want of a better figure it works out at close to 230 knots IAS before attempting to level out after stall recovery. If nothing else, in the heat of the moment it is a quick figure to work on since it is high unlikely the crew will have the time and inclination to go heads down into the FMC during a stall at high altitude simply to locate a suitable level out airspeed.
By keeping the body angle between zero to minus two below the horizon until reaching at least 230 knots IAS, you can should count on (IMHO) losing at least 3000 ft of altitude before reaching that speed. That assumes high power used in the process. That figure was from observations in a full flight 737-300 simulator