Yes and no. In a broad sense, "soilless" means doesn't contain any of the dirt/soil you dig up out of your backyard. You definitely don't want to use any of that stuff.

That said, a very heavy, peaty, small particle "soilless" potting mix that you can buy pre-bagged from walmart isn't much better.

Short of building your own, my suggestion is to go to a dedicatedplant nursery, tell them what you need and hopefully they'll have a bag made specifically for containers composed of bark, peat, perlite and maybe a little compost.

Have you seen any bags if LGM All-purpose Potting Soil? That works.

Possibilities are quite few:
Big Box stores and nurseries are loaded with POTTING SOIL(mix). Miracle Grow has several kinds, Viagro .. and many more. Most of those are PEAT MOSS based with some perlite and may contain some UNKNOW ingredients, as they do not publish what is in it.

Now that you are here check out and read all about 5.1.1 potting mix. In a nutshell, it is a bark-based medium ( 70% bark fine), as introduced by AL(tapla). With this one, it can get pretty much involved, b/c you have to mix your own.