As I understand things, wood has a largely tubular structure.
If you take a tube, suck out some of the air, then stick both ends in a liquid, the liquid will fill the tube from both ends only until the remaining air is at atmospheric pressure. If you have a pump able to pull down to 6 PSI below atmospheric pressurre, you will pull out 40% of the air (normal atmospheric pressure at sea level is 14.7 PSI. Rounding off to 15) and the liquid will penetrate about 20% of the way into the tube from each end.
A pump that will pull down to 12 PSI below atmospheric (3 PSI absolute) would give double the penetration: about 40% from each end for 80% total.
The degree to which the stabilization solution fills the wood is therefore entirely dependent on the vacuum that is pulled.
There is no substitute for a good vacuum pump.