Yes the better meters can have their probes left in the water in the same fashion as the monitors. Nearly all the professional model pH meters have a function where you just enter in how often you wish them to take a reading and they turn on automatically and take the reading, store it in memory, and turn back off. When you push the on button they then show the last reading and the time and date that it was taken. To see a record of recorded readings you just go to log and it gives you a list of readings with times and dates. If you buy, or recieve with a used meter the software disk you can also down then load all the data and make graphs, table, charts etc with the data. Or if you know how to program in basic you just write a simple program to down load the info into columns and then use that data with something like Micro Soft Excel. Nearly all of them do turn off by them selves after a few minutes of inactivity to save on batteries, however those models that accept an auxillary power input (wall outlet transformer) allow you to disable that function.
The meter I posted a link to is actually one of their cheaper models. It does not have an outlet to down load dat. It does not have an input allowance for a transformer so it turns off after 15 minutes. It also does not have auto program features. Basically it is just a very accuratte pH meter (0.001 resolution)with automatic temperature compensation, that also displays Temperature readings and ORP (mV) readings. It is also water proof to IP167 standards and submersible to a depth of 1 meter without leakage.
A meter with all the other features would start at almost double the price of the one shown.