It's very possible.
I do it at work all the time, especially for in the winter.
People with 19" rims don't want to run 19" runs in the winter, so we can downsize to 16-17", but adjust the tire size to have the same overall diameter so that the speedometer will not be off at all.
You just have to make sure that the smaller rim that you use has the proper offset, bolt pattern, proper hub fitting, and proper rotor and caliper clearance.
An example is newer 2 wheel drive Dodge Ram's with the "appearance package" use 275/55R20 tires.
Customers come in for winter tires and we put 265/70R17 winter tires and rims on them no problem.
As long as the diameter is within 3% of the original there is no adverse effects.
The example I used is less than 1% off in diameter, and the speedometer will be off by about 0.60 MPH, which is not even noticeable.