Ice Cream mango is excellent! I tried it at a mango tasting we had here in SoCal and it was perhaps the best mango or at least top three of the day. I think just about everyone rated it as #1, 2 or 3.
It is very sweet and it has a unique complex taste that is difficult to describe but it's absolutely delicious. Picking mangos here in California is different than in Florida. Depending on your location and climate, our mangos may need to hang on the tree a lot longer because we don't get as much heat.
In your situation where you only have a single mango, waiting a bit longer is better than picking it early. What I do is wait for the shoulders to fill in and when i notice the mango is not getting any larger and I feel it is about to fall off the tree, I very gently lift the mango in the palm of my hand until the mango is laying flat on my hand. I do this trying not to put any pressure on where the mango and the stem meets. If it comes off the stem, it should ripen properly. Don't try to force it off.
Alternatively if you want to get the maximum flavor. You may want to bag the fruit and carefully tie it to the branch so that if it drops off the tree, the bag will catch it before it hits the ground. If you think it's ready and it's still hanging on the tree, give it a gentle tap and if it falls off, it should ripen.
I am not currently growing Ice Cream but I will be grafting it to my trees this year. Please keep us updated on what you think of the fruit!
Simon