Can LabVIEW be used instead of an oscilloscope to measure signals?
Sort of, but you won't be really happy with it.
LabVIEW only replaces the display end of an oscilloscope.  You need a data acquisition card to take the place of the oscilloscope hardware - you know that since you've already picked out a NI DAQ.
The DAQ you picked out appears to be digital IO only, so it wouldn't be much good as an oscilloscope.
In any event, there's not a full featured oscilloscope program for LabVIEW that you could use.  You'd have to implement it yourself.
A good (and fast) data acquisition card from NI would cost as much as a (low end) regular oscilloscope - and the low end scope would perform better as an oscilloscope than LabVIEW and some home grown VI.