If the heater leaks, it is a good idea to shut off both the power and the water to it. The problem with TP valves is two-fold: it doesn't take much on the seals to allow them to leak - a little piece of rust can do it, and eventually they either clog up with rust/sediment or the spring weakens, and they leak or won't open when you need them to.
So, especially on an older HWH, it is a pot shot of whether testing the valve will require replacing it. Often, gunk gets under the seal from an older tank (rust, etc.) and it cannot seal anymore. Sometimes, if you run some more water out of it, you can flush out that crud, and it will reseal, sometimes not. From a conceptual viewpoint, I guess if you are going to open it, you should open it fully and let the water run for a little bit, you may be more likely to flush all of the accumulated crud out verses trapping it under the seal. But, if the shaft is all corroded or has mineral deposits on it, it may not move back into place enough to allow it to seal again. Opening and closing it may help, but may not. From a safety viewpoint, it is probably a good idea to check it per the instructions. Most people don't. They usually work. How often do you check your GFI outlets? You are supposed to check them monthly, too.