Will you be able to hear the system? Yes
Will it produce the same volume (sound pressure) in a much larger space? No, not without turning up the wick considerably
Will it (or any audio gear) sound any good in the space? Up close, yes, probably. Further away, impossible to say as the room acoustics will play a very large part in the way anything sounds
The bottom line is that the amp and speakers are good but the room size and shape trumps everything. Sitting at a similar sort of distance as you are at the moment will generate the same kind of localised sound level but you'll probably notice less bass, though it should actually be cleaner. You'll be running the amp a bit harder too.
More power rarely goes amiss. That Rotel has a whacking great donut-shaped toroidal transformer coupled with some hefty capacitors. While it may only produce 30W/ch, it'll do that all day long because there's a decent power reserve from the nature of the design. If this were a car then it would be an engine with a lot of torque.
That Class D or Class T amp from Ebay isn't 100W.... not in real life. The specs aren't complete but they're better than most other T amps. I'm looking at the Electrical Characteristics chart. The closest they get to a useable spec is "Output Power - THD+N<0.01% - RL=8Ω, f=1000Hz = 35W" It's not clear if RL means both channels driven or each channel measured independently and then averaged, but lets give them the benefit of the doubt.
What's more telling is this measurement is at 1000Hz (1kHz). That's a very easy frequency for an amp to reproduce so it's going to give a nice healthy-looking number. A real world audio frequency test is 20Hz-20kHz. Running at 1kHz as opposed to 20Hz-20kHz can boost the measured power by something in the region of 18-27%. Being generous then, that T amp is at best 30W/ch if you fit it with the biggest power supply it can take. It doesn't give you any real advantage over the Rotel.
A more powerful amp with a decent amount of dynamic headroom is what you need if you want to drive speakers to higher volumes safely. That's really the key. Speakers rarely die because they're given too much clean power. What kills them is amps running near their maximum and so providing lots of distortion in the signal. I'd have more faith in the Rotel to drive your speakers at higher volume than the T Amp.
A larger pair of standmount or floorstander speakers will generally be more efficient than small bookshelf speakers. You'll also get more bass extension. An amp that puts out a lot more "torque" will help you drive those speakers cleanly at higher volumes when you need to fill the space. A better solution for spreading the sound and retaining the fidelity would be more speakers - say in the kitchen and/or on the Mezz level. The room acoustics won't be such a big factor then compared to driving one set of speakers to try to fill the entire space.
