Monster-cross build on the road, will it be fun?
It will be a fun bike to ride, but it won't feel as fast as a road bike.

I've been building up variations of this bike for the last 15 years and there is simply no replacing the feel and acceleration of skinny tires and light wheels. Geometry also matters. Head angle, trail and wheelbase can be very far off the dimensions of a "normal" road bike. 

Much of the "feel" of a road bike is not it's absolute top speed, but it's ability to accelerate quickly and be nimble in it's handling. Any changes you make in tire width and geometry will be compromises. The question that only you can answer is "Is it good enough?".

Tire choice will make a big difference in how fast the bike feels. Tires in the 35c range are all over the place in terms of weight, tread and rolling resistance. A light skinwall 35c tire with smooth tread can be reasonably fast and certainly makes bad roads and the occasional trip off the road's shoulder much easier. I really like having a bike that I can easily pull off into a dirt should and not worry about loosing control.