It is indeed possible, but isn't a straight-forward affair. You could power the Raspberry Pi via the header pins (pins 4 & 6 for example), but in doing so, you are bypassing the input filter capacitors, TVS surge suppression diodes and polyfuse. In doing so... if you get them back to front... you will release the magic smoke genie.
The best way to do it using a multimeter (note before reading any further... your meter can only measure current or voltage... not both at the same time... so if you're not happy with this... skip to further down) is to get a sacrificial USB lead, and either just cut through it, and rejoin the ground line, or to carefully remove the outer insulation, and then work out which wire is the 5v/VCC one if you can (hopefully it is red!) and cut it so you can put your multimeter in-line with that when it is in current mode. Then you can plug it into the Raspberry Pi and power it normally, and be able to measure the current consumption.
However, the simplest, safest and in my opinion best way to do this, is to instead get yourself a different USB power meter. There are a lot of USB power meters that save the last reading when they power off, so they are perfect for testing USB battery packs. The absolute best one I have come across so far is the YZXstudio USB Power Monitor, which in addition to being very accurate, has a beautiful colour LCD screen for data and even graphs, lots of logging options, and the ability to send data via bluetooth! Making it perfect for something like logging Raspberry Pi voltage, current and coulomb counting via a script on the Raspberry Pi itself! You can find them on eBay for around US $38, but make sure you do choose the bluetooth option (as you can buy it without it) if you do want to do that.