Can I measure voltage and current at the same time by using two multimeters?

Yes, that works. However, keep in mind that no meter is perfect. Ideally, voltmeters have infinite impedance and current meters 0 impedance. Real ones don't, of course.

To the extent the meters aren't perfect, particulary the current meter, it will affect the system while trying to measure it. The current meter will cause some voltage drop proportional to the current. You have to be aware of this and possibly account for it. For example, if the voltage drop across the current meter is too big to just ignore, you have to consider carefully on what side of the current meter you measure the voltage, and whether your system can tolerate the voltage drop in the first place.

Yes, you can. No real draw back unless you get to very small fractions of a volt or micro amp ranges and your precision requirements are tight. Or very high voltages and currents that your multimeter wasn't designed to handle well.