A lot of switching power supplies have a Y capacitor between the primary and the secondary of the transformer inside, in order to reduce EMI. So there's some very small amount of current flowing and in some cases you can even feel it if you touch the connector, but it's low enough that it's extremely unlikely to even get more than a buzz or some sparks.
But just the presence of that connection could affect the isolation of the multimeter, or affect it.
And even if there's no such capacitor or you remove it, you'd still have the switching ripple (you'd see the voltage fluctuating at a high frequency if you'd have an oscilloscope), unless the switching power supply has a very good output filter (at least a capacitor - inductor - capacitor)
Linear power supplies ( old style, low frequency, transformer -> bridge rectifier -> bulk capacitor -> (optional but highly recommended) linear regulator
would be fully isolated and should not affect measurements in any significant way.
later edit: Another suggestion would be to make sure everything's extra isolated by using one of those digital isolator chips, like the expensive Adum5000 for example:
http://www.digikey.com/product-detail/en/analog-devices-inc/ADUM5000ARWZ/ADUM5000ARWZ-ND/1972297The chip in the link above takes in up to 5.5v DC and outputs 3.3v or 5v at up to 100mA with a lousy efficiency of 33% ... which doesn't matter since you wouldn't use it with batteries. It's more important that it's small and could very well be placed inside the multimeter in the place of the battery and have just a DC In jack on the battery cover or something like that.
The current is also not a big deal, since the multimeter won't use more than maybe 3-4 mA.