You will probably not see him for 2 days after he eats, since he's digesting. Depending on the snake, you might not see him during the day much, since they're nocturnal. I wouldn't put him right beside the TV, if you can help it, but in the same room should be fine. I usually wait until I've gotten at least 2 meals into them to start handling a bit, but even then, I would just go really slow, not doing any major amounts of handling and not every day. Some will say to leave them alone longer and I don't think that's a bad thing. You've got many, many years of handling ahead.
To answer your question, will he eventually not be so shy, that totally depends on the snake. Some are out a lot, some not so much. I have one that's out and about a fair amount, but she's actually the one who's a little more skittish to hold. Some of mine that hide more are more mellow to hold. They all tend to be out and about more when it's getting close to feeding day and I use this partly as a guide of how much to feed them. If they aren't cruising a bit, I may delay feeding.