The short answer is yes. The helpful answer is probably much more complex.
If you want to use a monitor you will want to design the system so the subs do the heavy lifting. IOW the higher the crossover point the better.
Your concern about a 6.5” woofer being able fill that large of space is legit. Speaker makers can design a very small box and cone to cycle quite low but I have yet to hear one do it at realistic volume levels.
In my opinion, depending on what types of music you listen to and how loud you listen to them, I would cross the subs at no lower than 80 Hz and preferably closer to 120 Hz and if you really like it loud probably higher than that.