I did my share of in circuit measurements for QC reasons, and I never saw anything damaged by a multimeter that way, even when using a desktop multimeter. You should note, that to damage a component, you usually need to heat (pars of it) up, so it breaks. even 10V some mA is only a few mW, barely enough to heat up anything, including internal diodes and such. 0603 components are rated for 63mW. The DMM will not send enought power to it.
When you test something under power, that is a different story. You can permanently turn on a MOSFET for example, and break something, or latch up parts of the circuit. But I would not be worried about it.