If you search the archive on this forum, you'll find more than you ever wanted to know about stabilizing wood. There are also a few key points missing.
Stable is a relative word. Yes, it would be more stable than when it started - but not very.
To get good penetration, you need vacuum and pressure. Now while I was cheaping out investigating this idea, I tried the following.
Put your sealant (I used thinned varathane) in a sealer jar. Warm it up in hot water as if you were making preserves. Add the wood and seal it shut. Put it in a snowbank. No snowbank? Icewater? Freezer? As the remaining air shrinks with the cold, you'll see bubbles coming out of the wood. This indicates there is a vacuum. Leave it in the cold overnight. Next morning, still in the cold open the lid and let the cold air in. Close the lid tight again and bring it all inside where it's warm again. As the air warms up, it expands and you get pressure. Leave it this way all day and then take the wood out to dry.
I got all the way through 5/16 inch maple this way. I wasn't, however, particularly happy with the varathane treatment. I guess I'm just spoiled by the professionally done polymerized stuff.
I now have a vacuum pressure chamber which I put together for about $100 Canadian. Now I can get good penetration in reasonable time, through over an inch of wood but I still haven't found the product I like.
Good luck - and share your results.
------------------
Rob Ridley
Ranger Original Handcrafted Knives
http://www.col.ca/rridley