I've done it but it never works really well if there are many grasses and/or other sod components. Rye will grow lying on BARE SOIL, with adequate moisture, The mowing may help keep the seed moist, but unless it can get on the soil, it may germinate and die off.

If you have a good solid clover plot, another decent method of seeding in a grain is to mow it tight, disk with a heavy cut after the next heavy rain, broadcast the fall grain, and cultipack. Its is important that the clover is well established for this method though since the disking will set it back a few weeks due to the heavy cut on the roots. It only works well if the disks can get an inch or two into the soil. Dry disking in grassy sod will do almost nothing to get rye (or clover) in the soil.

If you have space and time, I'd suggest leaving the clover plot alone, and prepare a separate plot for a fall grain.