It WILL effect the trajectory of the arrow, but it depends on a few factors -
In my experiences (including the mechanical kind), the largest factor is the cut pattern in combination with the fletching type.
A broadhead with more than two cutting surfaces will open the mesh much wider than a single blade head. This is important when using a non feather fletching. The higher the profile of the fletching, in combination with the stiffness of the fletching, can introduce error as the arrow leaves the blind.
I noticed these effects greatest while shooting small diameter broadheads (1") while using high profile plastic vanes. In yardage over 20yrds, the effects amplified immedately, to as much as 15" at 30 yrds. BIG DIFFERENCE in point of aim/impact.
Using feathers you'll be at an immediate avantage as they can lay down passing through the mesh, but still use a multi-blade head as much as possible!
Keep the mesh tight, and you'll be fine.