Seriously? You think there's that kind of bandwidth available? YouTube is entirely out of the question. The power simply isn't there for on-demand internet type applications. You'd have to code a specialty transmission protocol so that your transmitting antenna doesn't waste power trying to communicate instantly with a "last mile" located millions of miles away. You'd even want to limit (or eliminate) video transmissions to preserve power. Even for DirecTV, you'd need to reconfigure a few satellites and power them waaaaaay up. It's a long way to Mars, and we don't typically transmit at sufficient power to get TV level bandwidth all the way there.
While our deep space probes can accept higher bandwidth streams, they transmit at modem speeds to limit transmission power. There also has to be a lot of error correction (basically sending more than the minimum number of bits), which also cuts down on bandwidth. Unless you want to spend your electricity on transmission, instead of stuff like life support, you're going to be limited in your bandwidth for web applications. Probably limited to 0, if you want to maximize mission success.
All this stuff also assumes the mission is performed while Earth and Mars are within line of sight. There's a good portion of the year when communications between planets is impossible because you'd have to communicate through the sun (more properly, the sun's magnetosphere, which would effectively scramble any comms).
Basically, unless you want to waste resources on what is essentially entertainment, you have to wait until there's sufficient infrastructure on Mars, set up local data centers, and periodically sync data from Earth. Presumably, you'd just perform periodic syncs, instead of direct access, since the Sun would still be an impediment, and you'd have a minutes-long delay anyway.
If we get some sci-fi like instant communication scheme, of course we might manage something.