That said, I do believe that Sam is in love with Frodo in a platonic sense of that term. Does that make sense?

Absolutely! I think it's a great, rare example in film of a friendship in which two male characters are shown to love each other deeply, and completely platonically. A great deal of their love for each other, I think also probably has to do with how each one reminds the other of home and the Shire, and the life and world they are trying to save.