The quick answer is yes, this would affect your ability to use LabVIEW 6.0. You would not have Traditional DAQ functionality in LabVIEW 6.0 after installing DAQmx 8.1.
NI-DAQ 6.8.x is a Traditional NI DAQ driver (The earliest version of DAQmx was 7.0). DAQmx 8.1 will not work with that version of NI-DAQ so you are right that you would need to uninstall the 6.8.x version. Since DAQmx does not have support for LabVIEW 6.0, you would lose your DAQ functionality all together for LabVIEW 6.0 if you were to install DAQmx 8.1.
There are versions of NI-DAQ that have Traditional and DAQmx included, and that have Traditional support for LabVIEW 6.0. You can find a quick reference list at the following page:http://digital.ni.com/public.nsf/websearch/97D574BB1D1EEC918625708100596848?OpenDocument
Note: The Traditional Driver is supported in LabVIEW 6.0. DAQmx is not supported at all in LabVIEW 6.0, but you could find a version that will allow you to have both on your computer at the same time, and still have Traditional support for 6.0.
Hope this helps!