@ohihunter2014: Been there, own the rifles, got the t-shirt.
Old picture, need to take a new one, but take a look here - the 4.5-14x40mm Buckmaster is ALMOST touching the rear sight at the front, but there's a mile of air under the tail of the stock above the comb. Pretty sure that's a Weaver with Millet (CHEAP CHEAP) low rings, they might be mediums. You can see the top of the comb vs. the top of the cheek riser, and the top of the sights vs. the centerline of the scope. Before I changed to this Nikon Buckmaster, I had a Bushnell Elite 3200 on top, which is in the second picture, and I remember I couldn't get the scope covers onto the objective because they hit the rear sight.
You might be able to drop a straight tube optic - meaning like a 1-4x24mm without a belled objective - a bit lower, but like I said, I'm pretty sure these are low rings, and there isn't a lot of room to drop the scope before the tube is resting on the rail itself, which would buy you only about 1/4", and the optic would still be WAY high over the top of the comb. Even if you laid the belly of the scope right on top of the receiver, you're talking about a half inch of comb height difference vs. the irons, so even adding 1/2" of mount and ring height with a straight tube scope puts about an inch difference between the two. Unfortunately, that would mean with the scope - likely when you were making your longest shots - you'll be floating your cheek weld to reach up to the scope. And of course, you're talking about something I haven't seen for mounts and extra low rings to get yourself down that low with a straight tube scope - maybe a set of rings with integral bases? And of course, that doesn't account for any clearance for the eyebox over the hammer spur. I have plenty of room under my scope pictured here, but For any flared objective scope, like normal 3-9x40mm scope, forget about dropping any lower than what I have pictured below, it's just not gonna fit over that sight.
A guy can lift his cheek over an inch off of the stock to use the scope, but a riser is a much better option.
Here's the only picture I have of the older Bushnell on this rifle - you can see that the objective bell is even with the folded rear sight, and this was using low rings. For a 40mm scope, there's gonna be about 3/4" difference between your cheek position when using the irons vs. the scope, even using lows and a low mount. No sense in sacrificing cheekweld on your longer range shots.