Have I damaged my multimeter by applying voltage in resistance mode?
When multimeters are in resistance testing mode, they connect their battery to the output through a high resistance (maybe in the order of 200kOhm if not higher), and then measure the effect that the load has on the voltage - if the load is very high resistance, it will read close to the full supply voltage, if the load is very low resistance, it will read close to zero.

What this means is that if you connect a voltage source to the input in this mode, it should do no harm at all (unless it is out of range of what the DMM is specified for, which 4V or so definitely wont be) because the high resistance of the internal voltage source will limit any current flow.

TL;DR; no you won't have done any damage.



Update:

Even though this is the schematic of a fluke 87 multimeter, yours will likely be very similar. I've highlighted the switches that are closed for resistance measuring mode, and also for reference the high resistances that are protecting the input (and will mean you have not done any damage):