The pulse logger you are using sounds like the OM-CP-Pulse101 which is manufactured by MadgeTech for Omega. www.TheDataLoggerStore.com sell this product and others like it.
The MadgeTech dataloggers have the ability to show in real time the recording of data, all you need to do is have the interface cable connected to the logger and set the software to show real time recording, the logger can also be recording at the same time. You did not mention the distance between the logger and your computer. There are two ways you can connect between the distance, one is to run a wire from the meter to your computer and have the logger at the computer and connect the pulse wire from the meter and have the logger connected to the computer. The other way is to run a RS-232 cable from the computer to the logger located at the meter. Since the logger downloads at a rather slow rate, the distance you can run the rs-232 cable can be upwards of 300 feet. I think the best way is the first way.
Note, if you leave the interface cable connected to the logger and not to the computer, it will drain the battery of the logger, if connected to the computer, be sure that the computer is left on, the interface cable will draw its power from the RS-232 connection and not the logger.
This information provided by Tech Customer Service, TheDataLoggerStore.com