Not sure about the max input level of the Olympus LS-P2, as it's not a very common recorder around here at TS.
Yes it is possible to overload the mic input. If you find you are getting distortion, engaging the bass-cut on the battery box may reduce output level to the recorder enough to prevent the distortion, and would be appropriate if you cannot lower the input level of the recorder sufficiently to prevent distortion. In that case you can somewhat restore the lost bass afterwards with equalization if the cut is too much, but often not entirely (the basis upon which the general "don't use bass-cut" recommendations are made). However, doing so is far preferable to a distorted recording.
A complication is that with small recorders there is often a lower limit somewhere within the full range of input level adjustability, below which the input will still distort even though the meters no longer reach full-scale and indicate 'over' or clipping. That's a symptom of the analog input stage of the recorder clipping prior to analog to digital conversion, which is where the metering happens. Finding that "do no go below" input setting is something folks figure out around here whenever a new small recorder comes into mainstream use. Often the term used around here for that is "brickwalling" since the action of the meters tends to not bounce as much as one would normally see, instead sort of 'ceiling out' as if hitting a brickwall at some arbitrary level.
You'l need to try it with various settings to see what works. Expect a few failed test recordings before you really nail it.
Hope that helps.