No, and no.
The only way to electively upgrade a point reservation is to use more points. So if you're a renter you would potentially be using more of the member's points if you asked for and received a 1BR. There isn't a cash difference that the desk would allow you to pay.
Doing this would put you in violation of your rental agreement and potentially subject to litigation from your member who is renting- they agreed to rent you a specific category for a given number of points. You can't go and change to something else at the last minute, even if the hotel desk tells you a different accommodation would be possible. So please, don't ask for a bigger room.
This isn't just hyperbole. If I (for example) spent my 100 points for the year renting someone a studio for five days, then found out they had gotten a one bedroom at checkin, and had borrowed all my next year's points without my consent to get that bigger room, you'd better believe there would be consequences. It's just something a renter should never do, at least without a clear, written approval from their member renting the points ahead of time.
The only way a standard gets an upgrade to Savannah is if a room goes out of service for maintenance, there is nothing left in that category, and a room in a different category is available. Or, if in a different variation of the above example, you get the front desk to use more of the member's points to change to the higher view booking.
Otherwise this never happens. With
DVC (unlike a cash hotel) you get exactly what you book, nothing more or less, unless there is a maintenance type issue.
Please don't misunderstand my post. I have no reason at all to think the original question was intended to do anything nefarious with the rental. In fact, I'm really glad you asked on Disboards, rather than just trying to upgrade at the resort.
Just be aware that members have previously posted here a number of times about renters taking extra points without the owners consent, by changing reservation room size or view at resort check-in. This simply isn't a road you want to go down.
If you want the flexibility to change your reservations in the future, use this trip to consider whether your own DVC contract might be a future plan. Have a great trip!