Sure, you can capture a warm and intimate vocal take in a dead room. It won't sound exactly like Celine Dion, but you can get something reasonable from it. As you said, you would be adding it all in artificially. From the short listen I gave to your reference track, it sounds like they added it all in artificially, too.
She has an amazing voice and can give a great performance, so firstly, you need to copy that. She is most likely using a great mic and mic preamp. There are mics on the market with a reasonable price that will get you 80% of the way there. Same for mic pres or the mic pres in an interface. They're good, better today than say 10 yrs ago. Some might be great, but on the consumer level, none are stellar.
The recording engineer probably has her going through one or two nice compressors before hitting the board. To get that breathy intimate feel during the verses, you really need to crank up the compression. But doing so brings out some harsh artifacts, like lip smacks, hard consonants, gulps, and all the other sounds our mouths make that we never hear. Mic technique is key here. Celine most likely knows how to keep most of that under control. Then the compressors can help with reducing the rest. And not just any ol' compressor can do that. There are compressors out there that better than others for vocals. Then the mixing engineer is editing out whatever remains.
For the loud chorus parts, they are doing one of two things; either she's backing off the mic and the engineer is running her through a limiter, or they do separate takes for the choruses and completely change their set up. Different EQs, compressors, and definitely a limiter on her vocals. I'm betting on the second option.
Then for the effects, there is a delay/reverb thing and I'm pretty sure a 2nd reverb. A nice lush reverb with a wide stereo spread.
And she probably recorded her vocals in a million dollar vocal booth, but honestly, I don't hear it with all the other stuff going on with her vocals. Maybe that's why it cost a million bucks!!