It should be safe. The safety standards already assume a user is connected to ground, since that's the worst case in terms of probability of electrocution. You are supposed to be two independent failures away from getting zapped, already assuming you are connected to ground.
For equipment with a conductive shell, that shell is tied to ground. To get zapped, line has to get shorted to the shell, and the shell connection to ground has to be broken. If the first doesn't happen, then there is nothing "hot" to connect yourself to. If the second doesn't happen, then the breaker will trip.
For insulated equipment, the device often has no ground connection at all. However, things inside are "double insulated". Wires are insulated on their own, but then shell then provides another layer of insulation between hot and user. Any conductive parts then also have minimum clearance and creepage requirements from anything hot, and units are generally "hi-pot" tested and tested for leakage.
Even though you are supposed to be safe when grounded, it does remove one extra layer of protection. Supposed the unlikely failures do happen so that the case of a unit gets connected to line power. If you're grounded, then there is a path thru you, and you get zapped when you touch the case. If you weren't connected to anything else, you might not even notice you were touching something with live power on it.
This is why there are special rules in areas where people are particularly likely to be connected to ground via low resistance, such as in a bathtub or around any sink. In some jurisdictions, outlets in such areas must have ground fault interrupters. That's a special kind of circuit breaker that not only trips due to excessive current, but also when there is a imbalance of current going out one of the AC leads but not coming back on the other. The missing current must be going from the line side to ground via some separate and unintended path, which causes a ground fault interruptor to shut off the power.
So in summary, while you are supposed to be safe, you are one level closer to a the right failures causing you harm, although the probability of such a set of failures is low. If you plan to deliberately ground yourself regularly, it might be a good idea to replace all your circuit breakers with ground fault interruptor types.
Of course grounding yourself to somehow protect yourself against EM waves is silly, and can have the opposite affect in many circumstances, but that's another discussion.