If your stabilizer comes off straight/aligned with the bow, it's a useful reference point for limb alignment/centershot.

You can also rest the bow on the stabilizer or stand, as opposed to the limb tips which can affect how the limbs sit.

 

I understand that but I was wondering if it was possible to do this without a stabilizer

 

Yes. But you need a level. Recurve Limb Alignment, A Better Method?
There's also a way to do it with two arrows (I think John Demmer posted it somewhere) but I can't find it.
You could also use tuning forks.

 

E -

I'm not sure who says that (and frankly don't care).
Not all stab bushings are centered/plumbed perfectly, and I've set up hundreds of bows and never used the stab as a reference for rest/plunger/centershot.

Even limb alignment can be done with the Mark-1 eyeball.

Viper1 out.

 

This is a photo from limbwalker's thread Is your recurve setup "on plane" ??? which should get an award for outstanding contribution.

Placing two arrows alongside the grip, either under the grip or remove the grip and use the riser grip area. You just need to know if the surfaces are parallel.

I find this a quick an easy way to see if the string is centered on the riser without reference to a long rod, although it is also a quick way to see if your long rod is centered on the riser.