Is it cost effective? I mean roughly.

Very very cheap, as long as you're writing your lambdas as performant as possible we've costed our app at ~2c / user / month with heavy api / database / lambda usage

It seems you are estimating the costs per user. I think an estimation per request and perhaps compared with raw EC2 servers would make more sense. Anyway, it's encouraging to hear that's cost effective. My experience with managed/ server-less platforms is quite bad in terms of costs.