Yes, totally safe. The analog input still accepts 0…5V, and the ADC does not care.
However, you should not throw the ratiometric principle overboard.
The ATmega2560 runs at 5V, that is the same 5V as the 5V pin. The sensors should be powered with that 5V.
The sensor outputs a voltage relative to the 5V and the Arduino reads a voltage relative to the 5V.
If the internal voltage is used, then the Arduino measures a absolute voltage (because of the absolute voltage reference), but it needs to measure the relative voltage (relative to 5V).
You can get better results by taking many samples (5…100) and calculating the average.
If you want to detect small changes, than you can average them and calculate the result with ‘float’. The noise will help to get more resolution than the 10-bits. The overall accuracy will not increase.
I don’t know what you noise is like but in a situation where there can suddenly be high or low voltage spikes I found deleting the highest and lowest sample then averaging the rest can be quite effective.
When collecting a lot of samples you might delete 2 high and 2 low.
Another way to increase sensitivity and to keep some of the ratiometric behaviour is to lower Aref with a voltage divider powered from the 5volt pin.
So voltage divider between 5volt and ground, with the tap to the Aref pin.
And switched to EXTERNAL in setup() (don’t forget that part !).
But maybe the pressure sensor itself is not accurate/stable enough for that.
Leo…