FWIW, my TA has an opinion about online check in, in general. If you are flying, she says not to hit the online check in button until you are at your gate and about to board the plane. She says that if for any reason it looks like your flight might be delayed or there is a snafu in your traveling and you might not arrive at all the night of your check in, Disney has more flexibility to extend "grace" if you haven't started the check in process online.
Your TA is completely wrong, sorry. Whether or not you've done online check in has no effect on whether or not the resort can/will adjust things for you in a last minute situation.
To the OP, as others have said, doing online check in won't affect your chances of a free upgrade. Rooms are assigned 5-7 days before your arrival for the most part. If you are planning on putting room requests in, make sure you do online check-in at minimum a week before your trip. (If you called in your room requests, DON'T put any on your check-in or your previous requests will be removed.) Plus, putting your estimated arrival time really helps you. 75% of the time, my room is ready within 45 mins of the time I told them we'd be there, even when it's early. They do use that info when assigning rooms.
WDW Resorts are not like other hotels at all. Mainly because WDW operates at 85%-90% capacity, which is unheard of at a regular hotel. (DVC is even higher, more like 95-98% capacity). When WDW upgrades people, it's not usually just to "be nice", though that does happen on rare occasion. The upgrade because they need to - they've oversold lower priced rooms (happens a lot during the cheer/dance/sports events, there is a problem with a block or rooms or areas of the hotel, or there is a specific problem with YOUR room. Cheap rooms are usually full, so when they have to move someone it's usually an upgrade. So not only do they solve their problem, they get a happy customer who got "pixie dust" upgraded and tells all their friends how magical Disney is. And maybe they LOVE the upgraded room and next trip, they book it.
In 20 years of going to WDW, I have received 1 upgrade. But that's okay, because I book the room category I'm happy with. My clients have been luckier than me. LOL But regardless, my first advice to them is book where you want to stay. If a certain room type will make your trip magical, book it!! Don't hope for pixie dust and be disappointed. Make your own magic.