Yes the GH of the tank water will lower to some extent, depending upon the initial GH level. As for harming the fish, no, assuming they do not require hardish water. That depends upon the species and the GH.
On the mixing of source (tap) water and distilled: this is proportional; if you use for example 2 gallons of tap water mixed with 2 gallons of distilled water, the GH of the tap water will be reduced by half. When this mixed water is then added to the aquarium, the GH will be lower than it is with just tap water, but higher than it is in the mixed 4 gallons. This is because you are not diluting the water in the aquarium by much.
Ask if this is not clear; I find it hard to explain chemistry! And providing us with the GH for your tap water will also help us narrow this down more. And what fish species are in the tank.
If you start with all tap water in the tank then use a 50:50 mix of tap and distilled water at every water change, the GH of the tank will drop slightly at each water change until it reaches the same as the 50:50 mix. This gradual drop in GH won't harm the fish, unless you do the water changes very close together.
It's changing GH quickly that harms fish.
I have done this successfully. I usually change 75% per week. When I decided to drop the hardness I did a daily 20% change using the target hardness for the water I changed for a week. Therafter I went back to my normal schedule of 75% a week using the target hardness. By week 3 the tank was very close to the level I wanted and no ill effects whatsoever.