That implies exposure duration can be kept same for both formats. However both images should be viewed on same sizes. if you magnify stars start trailing.
Yes that ways the Image remains same.
Only some corners are cut
The magnification I mean is that viewing a cropped version on the same screen appears bigger.
But since I haven't tried that on ff, I cant confirm the exposure for the same.
But for my crop sensor 20 -22 secs max is what I found practical to capture still stars.
You may please confirm the practical shutter speed on ff which gives you satisfying results.
Just forget the 500 rule and try