1. I do not see a reason for a water change 'now'.
2. The presence of nitrate alone does not mean the tank is cycled (however it may very well be)
3. The usual metric (depending on the protocol) is if a tank can process 2 ppm total ammonia in 24 hours. I would put more weight on the fact that your tank only processed 0.5 ppm in 24 hours. (Assuming your testing is done correctly - and API is sometimes difficult to read - remember - the color (per the instruction) of the solution needn't be exactly at 0 for the measurement to be 0. If the color of the tube, in the proper lighting is closer to the yellow (0) than the light green (0.25) - the value is considered to be 0.
4. I would add ammonia to 2 ppm, (verify its at 2 ppm after you add it) - and then check again 24 hours later. I think that will give you a better idea of what's going on.
5. You can also take a water sample to your LFS and verify your numbers with a different test kit.
Just to get back to your original question - the nitrate levels in your tank may help to promote more of an ugly stage - especially if they go higher - so a water change of like 50 percent will lower them to 40 or so. It will not affect your cycle one way or another. If you want to do this, I would do it before trying the 2ppm ammonia test.
As
@JNalley suggests (and I agree) there are multiple protocols and methods to cycle a tank. In all reality, if you want to add fish - you are probably fine (assuming you're not going to try further testing). If you are wanting to add fish now, I would go slowly and I would do a water change. Just to emphasize - you don't want to add ammonia to a tank with fish - I know that sounds like a self-evident idea - but - it has happened before. Let us know how the tank is going, and welcome to the Hobby/R2R