Most receivers will but not at full power. Understand that most of the time, in a typical home theater with a powered subwoofer, the main speakers will be drawing less than a single watt during most of the movie. During loud peaks, you may get to 15 or 20 watts. What that means is that the amplifiers in most receivers are serious overkill for their intended purpose. With a 4 ohm load you could double the current draw from the power supply but that still isn't serious in most instances. If you get somewhere near full power output (extremely rare in a typical home installation) then you could exceed the power supply's ability to deliver current and cause the amplifiers to clip. You don't want that for sure. Same with 8 ohms speakers, by the way. It is just that the 8 ohm speakers will hit the wall at a higher power level than the 4 ohm speakers.
If the manufacturer provided a 4 ohm rating for the receiver then the "power" figure would be a lot lower and consumers seem to like big power numbers. So the manufacturers simply don't provide a lower impedance rating preferring to call an amp 100 watts per channel instead of 50 or 60 watts per channel. The amps with lower impedance ratings normally have stronger power supplies so they can simply push more watts out the door as the impedance falls.
There isn't anything magical about 4 ohm speakers other than the fact that they draw more current to produce the same volume as a higher impedance speaker. As long as you don't exhaust the power supply's current delivery, then all is well. There you go. Try it if you like. Buy a bigger amp if you don't want to try it.