Yes a clogged transmission filter can cause transmission shifting problems and could even lead to transmission damage.
The transmission needs the transmission fluid to flow freely through the transmission and transmission pump and when that transmission fluid is restricted the transmission isn't lubricated properly or cannot get the fluid it needs to work properly.
So if you notice shifting problems with your transmission check the transmission fluid level to make sure it's filled up properly.
If your transmission fluid is low it can also cause transmission shifting problems and even transmission damage.
If you're still having transmission shifting problems then getting the transmission fluid and transmission filter changed can help fix transmission shifting problems and prolong the life of the transmission.