Just a quick update!
I went to the local store and made a photocopy of a newspaper (I did not have anything else on hand). I then cut out the letter “E”, put a piece of nail foil on top of the E, and ran it through my laminator. As you can see in the picture, the foil stuck to the letter! Despite it being a success, I noticed that it is not scratch resistant like the embossing powder method, but more scratch-resistant than using double sided tape. However, I think this problem is existant with all types of foils (nail or craft transfer) when using this method.
Another thing I noticed is that the foiling was not clean. There were a lot of little specks of foil that came off itself and onto the paper. This, however, I am not sure if the problem is due to it being nail foils instead because I believe nail foils are a bit more thin.
Overall, I think from all my testing, nail foils are definitely a comparable but inexpensive alternative to craft transfer foils because it works just like the craft foils, but you get a lot more colours and designs! So give nail foils a try and create happiness with foiling on your cards today!