It should work fine. Ice cream has more to do time temperature and agitation. There is no custard or egg envolved. It needs sugar which would obviously be provided by your recipe. I'm looking at the ingredient list of Karo light corn syrup and it is useless.
- Light corn syrup
- High fructose corn syrup
To the best of my knowledge, nothing in that list contributes to the ice cream except sugar. The Karo sryup tastes to me mostly like sugar water with a very slight vanilla addition. Whatever taste difference is missing between the Karo and your alternatate syrup recipe is, in my opinion, going to be overwelmed by the banannas, cream, lemon and vanilla.
By far the most expensive ingredient is the vanilla bean and so why not first trying making the ice cream substuting a teaspoon or two of pure vanilla extract?
I hope you let us know how it turns out.