The short answer is yes.

I did exactly this with vinyl clad Andersen Casement windows and the trim was up close to the windows and when they tried to expand they had nowhere to go. It made the windows stick  and not fully close in the summer.

And make sure you do not block any weep holes in the window.

Back in the late 1950s, when aluminum storm windows were brand new to the market, our neighbor had them installed.  The installer was brand new to the installation of these brand new to the market storm windows. 

He did a very tidy job of caulking all around. 

Four years later all the primary windows had to be replaced because of water rot and all the framing directly under the windows had to be replaced too. 

There was probably mold too, but no one knew about mold back then. 

In any case, I remember as a young child "Never caulk the weep holes".

After college I bought an Alfa Romeo Duetto Spyder (the car from the Graduate).  It was really pretty, but they had the reputation for rusting out the rocker panels.  I asked my mechanic to drill out 1/4" diameter holes at the bottoms of the rockers panels.  They did have weep holes but they were already blocked and water drained out when he drilled them. 

But my car never rusted. 

My father had a Jeep Wagoneer.  He got a flat in the dead of winter.  When he went to remove the spare he found that the rocker panel that housed the spare was filled with water and frozen solid.  So he had the same mechanic drill weep holes in his car too. 

My brother-in-laws Acura Legend had a sunroof that leaked.  We snaked out the weep holes and the leak was fixed. 

You can never make anything 100% waterproof.  But you can usually arrange for drainage.   

Are you using wood brick mold or resin brick mold?

When I use the resin material I like to use the bonding agent they sell on the miters.  It keeps the miters tight.  White caulking for all the nail holes. 

The resin never splits so 15 gage nails, even near the edges are not a problem.

Lately the resin molding is cheaper than wood (in some shapes and sizes).

I'm not a window installer, but I like that idea.  It will always be snug to the window.  Never sloppy. 

I think the adhesive is like the old Testor's model glue which actually dissolved the plastic a bit and then "welded" the plastic pieces together. 

I think it is basically the same but they have added some white pigments.  Of course you don't have to paint this stuff.  But if you do, you need to use 100% acrylic for the paint (or the primer, or both) for good adhesion. 

White caulk matches the molding nearly perfectly.  When I needed white paint for the surrounding area, I matched the paint to the caulk so there is no obvious seam where the paint and caulk meet.