tl dr - To directly answer the question, SeaFoam is a pure petroleum product. If an alternative product is made up the same as Seafoam, then I'd think it would work just fine. If its makeup is not similar, you probably won't see the same results. Below is what you are looking for and a recipe for making your own substitute.
I found this answer for a SeaFoam substitute online with a very nice write-up.
Basically, the guy broke down what SeaFoam is by looking up the formula on Material Safety Data Sheets. This boils down to three parts: pale oil (ie: diesel fuel), Naphtha, and Isopropyl Alcohol (IPA). Note how all three are petroleum based in one form or another. This is the same as what SeaFoam claims for their product. His suggestions as far as how much of each would be:
4 parts diesel
2 parts naphtha
1 part IPA
The IPA he suggests needs to be fairly pure IPA and not what you purchase from the drug store. His suggestion is Iso-Heat, but I'm sure that most of the gasoline drying treatments are probably right in-line with this product. Read the back label and get the highest % you can find.
He suggests this worked very well, had nearly the same specific gravity as SeaFoam, was the same basic color as SeaFoam, and did not separate (just like SeaFoam). His write-up seems fairly comprehensive and makes a lot of sense. It sounds as though he's done his research and has come up with a viable alternative. This would also be a lot cheaper than buying SeaFoam, though I haven't found it cost prohibitive.
NOTE: While this may or may not be exactly what SeaFoam is and may work as the author suggests, you will want to make/use at your own risk. I take no responsibility for anything you do to your own vehicle.
EDIT: - As an aside, I prefer this write-up on using Seafoam. It is very complete, understandable, and (weeeeee) has pictures!