Are both the following constructions acceptable?

1. He agreed to work on Sundays.
2. He agreed to working on Sundays.

My query is basically regarding the second question; the first one is obviously correct; I have put that just for the context.

I think that in the second sentence, the words "the idea of" have been omitted, and the whole sentence is "He agreed to the idea of working on Sundays". Is the omission of words acceptable here?