It depends on how well you are able to manage your heat spikes in the green house. For every layer of protection you provide, you increase the micro-climate 1.5 growing zones. If you are able to put a thermostatically controlled vent in your green house to vent off the extra heat, you might succeed. The big issue is: Your tree will need to go dormant, AND it must stay in dormancy until spring time temps (whether in green house or outside) are stable enough to prevent freezing of newly budded leaves, and especially any blossoms. I would fear that a bit of a heat spike at the end of Persephone months would draw your tree out of dormancy, only to be hit by an other cold snap. If a cold snap hits when sap is flowing, it is likely to split the trunk, resulting in loss of the tree. You might want to spend a season or two getting to know the idiosyncracies of your greenhouse before putting a peach tree in there.
I think, you might do better by putting a peach tree on the warm side of the house, where you already have a good micro climate outside. Lay some 1" styro-foam on the ground around the base of the tree, allow a 6 - 12" window around the trunk, and extend the styro-foam to the drip line of the young tree. Plant some garlic bulbs and a few daffodils in the "window". Mulch the tree well, but keep the mulch from actually touching the trunk of the tree.
What are your lowest winter temps? How much work are you willing to do to keep this tree alive? If you are willing to go the extra mile, you might consider wrapping the tree in burlap when temps are consistently below freezing. If the micro-climate against your house or a similar building would place the tree at risk of having rain and ice from eaves causing an issue, you might consider pruning your tree into an espalier.
An other option would be to do a dwarf tree, keep it potted (think 1/2 whiskey barrel). If your home set up is such that you could progressively move the tree to a cold but protected area (covered porch or garage) then when temps there get nasty, bring it into the house. Only you know what temps you will be able to provide. It could be that the tree if placed in a huge foam pot would survive quite well in your garage. Then, when things start to warm up outside (when you see native trees breaking dormancy) you could move the tree outside.
Don't spend the money on a peach tree unless you are willing to experiment and fail! And even then... I'd recommend that you buy a bare root specimen instead of a potted tree.
Look at the recommended planting zones for the tree you are considering. Look at the Winter temp the tree is zoned for, then, consider if you can provide a micro-climate that meets that requirement.