This is totally anecdotal , but I have always liked to tune with a tuner and make sure that I was right at 440. After doing this for a year or so, I could usually feel if my group was higher or lower than 440, but it wouldn't bother after a minute of adjusting.
For me, I have always understood playing in tune as a sort triangulation between:
- Relative pitch
- A Weaker sense of of absolute pitch
- Muscle Memory
Being consistent with correct pitches helps with the absolute pitch aspect of this "triangulation".
Practice Makes Permanent:
I have always regarded "practice makes perfect" as a load of malarkey. All practicing does is ingrain things and make you better at doing them. If you practice do something something wrong, you get better and more used to do it wrong. Therefore I would recommend that you can tune your piano.
But, still be flexible:
That being said, you can take this too far very easily. Another valued trait in a skilled musician is flexibility. So although I would say it is better for your ear to play on a tuned piano as much as possible, you don't want to go to the other extreme and be unwilling or afraid to practice on an instrument or situation that is not perfect.
Lastly, Pitch is learned:
In a sense, equal tempered tuning is "wrong" according to overtones. But to most western ears it sounds right. This is also true of some world music that uses alternate scales. So this might a source of evidence that playing something that is out of tune for extended periods of times (Say, at least a month) is probably not a good idea.