The answer here is yes. When you donate more, it adds on to your current donation and when you reach a requirement for the next tier, you get upgraded to that tier.
I've had that experience because I was a Tier 4 supporter for a while (I didn't donate though, I was given it by someone who won it in a contest) and then someone like, donated $5 to make me Tier 5. Tier 4 basically starts at $20 for example, and the $5 I was given reached the $25 requirement for Tier 5.
Here are the minimum donation requirements for each basic tier:
Tier 1 - $5
Tier 2 - $10
Tier 3 - $15
Tier 4 - $20
Tier 5 - $25
So, if you donate a little extra, and you reach one of the requirements above, you get upgraded to its corresponding tier.