This is really funny because I am from Toronto (Sea Level) and flew to Denver a couple months ago and climbed Bierstadt the morning after arriving followed by Quandary Peak the next day.
Upon arriving in Denver I drove to sleep at 10,000ft then woke up early and climbed Bierstadt.
Will the effects and onset of altitude sickness exacerbated by the short time-frame involved and the drastic change in elevation given what her body is acclimated to?
Yes, I certainly felt it and I am a fit cyclist and rock climber. Towards the summit I had what felt like a belt around my head and it was slowly being tightened.
Most questions relating to altitude sickness agree that the best way to acclimate yourself is to go to high altitude regularly. Given that this is not an option, is there any way to mitigate the risks somewhat?
You can try Diamox, which is an epilepsy drug used by mountaineers to help acclimatize. I have used it before, just makes you pee a lot. From what I understand you do not take it to make a one day trip better, you take it for ten days while gaining 1,000ft elevation per day to prepare for a climb like Denali.
Her other option is to improve her cardio prior to coming. Run Run RUN! The fitter you are the easier it will be to acclimatize, but don't be fooled ,even the fittest coming from sea level feel it...
If she climbs the mountain the day after she arrives, will this make much of a difference?
Yes, every second at altitude the body is adjusting. Ideally she would want to sleep at 10,000ft the night she arrives. The climb will only feel worse if she sleeps at 5280ft. An alternative is on the day of arrival to do a small workout and then climb the next day. The small workout will help acclimatize.
Now for the disclaimer
I am not a Doctor, everyone is different! Everyone's body reacts differently to altitude. This is only my personal guess based on my own experience and the fact that it's the easiest climb in Colorado. This also assumes she is in good shape!
There's no doubt she could summit on the same day of arrival, my guess is she will experience shortness of breath towards the top due to altitude and exertion, she will most likely have a headache towards the top and she will most likely wake up the next day with a bloody nose.
The best way to ensure success is to pace yourself, breathe every step, take it slow and steady, bring lots of quick carbs and 250ml water every 15mins and stay positive.
PS. Sorry if this answer seems like it was written for a beginner I have no idea what your experience or your sister's experience is, I just tried to provide a good answer for anyone who reads in the future...