I am not quite following what you are asking / suggesting. To hopefully help, I will explain what we do in more detail.
Hit Points:
- No different than standard 5e.
 
- Calculated the same and function the same.
 
- Recovered that same (or whatever rest and recovery variant you want)
 
Bloodied Hit Points:
- These are a separate fool of "vitality" points.
 
- They are based on size x (Str mod + con mod).  Medium is (1), so for PCs: 1x (Str mod + con mod).
 
- These do not increase w/ level.
 
- You only take BHP damage on a critical hit (which is target AC +10 or save DC -10) or after your HP = 0.
 
- You die at 0 BHP
 
- Natural recovery of BHP is 1 BHP per extended rest (1 week) with bonuses (in time and or amount of recovery) for successful medicine checks and barber's tools ( healing kit, etc.).
 
- BHP can be recovered by magic at the rate of 1 BHP/ 10 HP of healing magic.
 
- Armor DR only comes into effect when you would take BHP damage. The BHP damage is reduce by your armors DR.
 
So we have a separate pool of vitality points; however, it more than just another pool of hit points. Simply drawing from those to restore HP wouldn't achieve all of what we are doing with BHP.  If I understand what you are suggesting / asking.