If the VOY crew couldn't adapt to anything in the DQ or be able to figure out how to use Alien tech, they'd look like total morons compared to all the other Trek shows.
Using alien tech is I think exactly what would happen, but it would be more interesting to show that as clearly different to business as usual with shiny starfleet-issue gear. Different deflector, nacelles glowing a weird colour. Engine room full of jury-rigged components. Some new weapon that isn't a torpedo or a beam. Some things giving out at really bad times, others adding unexpected new capabilities. and so on.