I have just over 78% Nitrogen in my tires. Otherwise known as the air we breathe.
In a consumer car application, it's mostly a money-making scheme. In other words, most places will charge extra for a 'Nitrogen fill", and the benefits are overstated.
Nitrogen molecules are larger than Oxygen molecules. So there is a slight benefit of possibly not losing as much air pressure in your tires over time if you inflate with Nitrogen.
I've heard some claim that the pressure inside the tire won't vary as much with pure Nitrogen, as compared to the air we breathe, which as previously stated is already 78% Nitrogen.
Tests I've seen indicate that the pressure inside the tire varies almost exactly the same amount between the pure Nitrogen fill and the 78% mix we breathe, when both tires are subjected to the same ambient temps.
Another consideration with filling with ambient air, is that over time, as the smaller Oxygen molecules potentially leak out, and we put more air in to compensate, the percentage of Nitrogen in the tire increases over the 78% that was present, when it was first filled.
Places that fill tires with Nitrogen, mount the tires and inflate them in the open air. So you'll never get 100% Nitrogen, because when mounting the tire ambient air will be present in the tire. The only way to get 100% Nitrogen, is to mount and inflate the assembly in a vacumm, devoid of any oxygen.
The only application that really benefits from a Nitrogen tire fill, is in aircraft. Because if there is a fire in the Plane at altitude, and the tire burns and bursts, the last thing you want is oxygen in the tire itself, contributing to the blaze.
Just for the sake of the discussion, I've studied Nitrogen in tires extensively, looking for any possible benefit that might positively affect our results on the Racing Team I'm a part of. In our extreme use case, it didn't matter one way or the other.
The bottom line for consumer cars is that it certainly won't hurt anything to get the "Nitrogen fill", but any benefit is so slight to nearly non-existent, that I'd only do it if they did so without charging extra.
To answer your question, there will be no problem adding regular compressed air to your tires, if the pressure in the tires drops.