You dont "need" to do any water changes during a fishless cycle.
It depends on what you mean on dirty. You are dosing ammonia which is toxic for fish, but you dont have any fish. Doing water changes will just remove the waste that you need in the water to fuel the cycle, so you would end up having to redose ammonia to replace what you removed.
If you overdose on ammonia you may need to bring it down with a water change. Ammonia above 6ppm is commonly cited as being too much and will kill the bacteria you are trying to grow.
You may want to keep your water parameters to readable levels, so if for instance, your nitrite gets too high for your test to read you may choose to change some water to bring it down to a readable level. This isnt really needed, but might be something you want to do so you can see more easily whats going on.
The nitrogen cycle uses up carbonate hardness (
KH) to convert ammonia into nitrate. Once its gone your cycle can stall. If you have low
KH in your tap water you may need to replenish
KH and a water change is one way to do this. But this is rare and unless you have reason to believe your water is low in
KH i wouldnt worry about that just yet.