Micros 3700, 9700, and e7 all update in real time. Real time can be a few seconds from when it is changed at the server/host PC until all the terminals pick up the change.
If you are looking to modify the price in a 3rd party software and pipe it into the Micros system that can be a lot trickier. I have seen it done in 3700 and 9700, but never e7 and I doubt that it could be done in e7.
To do it in 3700 and 9700 you would have to have some sort of export out of the 3rd party system and format it as SQL statements to pump into the 3700 or 9700.