No, you cannot interchangeably use the two phrases.
I would like to swim.
This holds more reservation. You are not sure whether you will actually swim.
I will like to swim.
This communicates the expectation one has.
Furthermore, there is statistical evidence from ngrams that in general you rarely would say "will like to". There is a 222 to 1 ratio likelihood for "would like to" against" will like to" in English books indexed by Google ngrams.
Interestingly enough there is a difference between the American and British frequency ratio. American has a 218 to 1 ratio while British shows 182 to 1 ratio.
Even more interesting the usage of "will like to" has increased by more than 130% between 2001 and 2008 in British books while the frequency of "would like to" slightly decreased.
In that same period the usage of "will like to" has increased by more than 140% in American books while the frequency of "would like to" kept relatively stable.
Maybe your friend is on to something. Maybe one day...