I've done this for years but only in the right setting. On a society gig you may be able to get away with some Beatles and Stevie Wonder ala Isn't She Lovely. Please remember that "Shadow of your Smile" is just barely older than a lot of the repertoire the jazzholes call into question. A good tune is a good tune. Period. Play "Blackhole Sun" on a bar gig and see how the girls all of a sudden start paying attention...
We can also fall into the trapping of trying to make a tune that isn't as good more relevant by cramming "modern" harmony into it. There is a way in which these over-arranged versions of "newer" tunes can sound convoluted and overwrought and leave a bad taste in EVERYONE'S mouth.
The only real way to know is to try them. Miles got crap for playing pop tunes. For most of the history of "jazz," pop tunes were all we played on the majority of our gigs.
I actually carry a "pop book" in the car just in case the client asks for us to "pick it up." Wedding planners and event coordinators love hiring bands that are flexible enough to whisper behind cocktail hour and then pack the floor once the bar opens up. My groups do that all the time. Ca-ching.