It's not necessary to treat them if they're basically sound. The problem is if your new cap simply goes on top of the post and can let rain in. If it were me, I'd be caulking on top of the post before putting the new cap in place, and then running a bead of caulk all around the joint after the cap is mounted. Even better is to use a metal cap that overhangs the top edges of the post so you don't have to worry about water getting in.

If you treat the open end grain on every post with Minwax wood hardener (even if the wood is solid) you will greatly limit its ability to absorb water.

The hardener is resin in solvent and will soak into the wood and fill in the many paths water can take to penetrate.
When you first put some on you can watch it just disappear into the wood.
Wait a few minutes and apply more hardener.