Personally seen a LOT of threaded fasteners used with acrylic windows lead to cracks in the windows. It can be done, but there are some important things to remember:
1) Oversize the hole slightly so there is a bit of room for the plastic to grow with temp change.
2) Use large headed cap screws or smooth fender washers under the head of the screw. NEVER use countersunk (flat head) screws with acrylic.
3) You want your screws to squeeze the acrylic against the liner, and hold it in place by friction between the large screw head and the liner. You do NOT want the screw to be preloaded against the side of it's screwhole (hence the oversized hole).
Lots of people get away with surprising things with acrylic but the fact of the matter is it varies in hardness and toughness from batch to batch, and it is known to crack when subjected to extended local stresses (Like screws).
I'm also curious - how are the screws themselves sealed so that water cannot seep down the threads and into the wood, since the screws go through the liner.