You can but only ECS screen modes will work. like DoubleNTSC/PAL, Multiscan, Productivity but NTSC/PAL will not work. So early startup, and games will not display. Some very rare monitors, like the one I mentioned a few posts up, will scan to all 15KHz screen modes! Try to find one of those. I think there are some BenQ LCD's that also work, use Google to find out more on this topic.
This is partially incorrect. If your monitor only syncs to 31KHz screenmodes (i.e., most modern monitors), DoubleNTSC/PAL, Multiscan, and Productivity modes
should work. Or at least are supposed to.
The only problem is you won't be able to see your Workbench to select those modes, since natively it boots up with a 15KHz screenmode. Also, as TjLazer said, Early Startup and most games, etc., won't work because they use 15KHz screenmodes.
http://amiga.lychesis.net/knowledge/ScreenModes.html