Nope, I've tried that before. Back in the good days that was considered "fair use" but fair use does not really exist anymore.
Back in the good days the idea behind copyright was good, it was to protect the artists. But now the artists are out of the picture, and it's to protect whoever owns the rights to the content. Big corps. The artists hardly get anything either. It's nice to see that more artists are going independent now though. Here's hoping this continues. The big corps need to die off and music needs to be considered art and not a product.
Even ignoring record company involvement, it was never OK to use copyrighted works without permission in something you made unless you weren't making money off of it or the work incorporating it and it didn't cheat the artist out of direct sales (substitute for a sale). If the artist made it clear that such uses were allowed with proper attribution (most Creative Commons uses, for example), then it's fine.
Uploading an old episode of Family Guy and putting "Copyright Seth MacFarlane/20th Century Fox Broadcasting Network" or "I did not make this and claim no credit!" does nothing for legality and never did. Some stupid kiddies thought that it did and started putting it on their infringing content prompting many others to do the same. The misconceptions probably originated from authors arguing that certain unauthorized work further damaged them by not giving credit or being made in a matter that reflected poorly on them, attaching their work to something they disapprove of. For example, Matt Stone and Trey Parker were furious when they realized that Michael Moore had put a South Park-style animation right after a selectively-edited interview with them that made it appear to be from them and appear to represent their position on the issue. Can you imagine how much worse it would be if they used something Matt and Trey actually produced without permission to do that? I certainly would not have hesitated to sue.
Many artists have bemoaned their songs being used during political events because it could be seen as an endorsement of a party or candidate that they disapprove of, so event organizers have to be very careful to get the public exhibition permissions through proper channels.