The way I read this, you're not going to store any other car ON the lift, 'just going to park the GT under the raised hoist ramps until you need the hoist for service work. Assuming the garage door doesn't say "hello" to the posts when it's opened, you shouldn't have any problem...and simple measurements and math will tell you if there's going to be an issue with that.
One would think the ramps should be well out of the way (vertically) for getting in & out of the GT when they're in the "up" position. The only clearance 'issue' you might have is clearing the distance between the posts (width-wise) when driving under the hoist. The GT is listed at 77" wide (round figures), so check to make sure the 'posts are further apart than that.
(Edit: Most overhead garage door tracks [I'm assuming you have the overhead type] can be adjusted a couple inches in regard to how far beneath the ceiling the door hangs when 'open'. If you find you need juuuuuuust a bit more vertical clearance for the 'posts, you ought to be able to arrange it. How far into the garage you can locate the hoist will also help as far as 'post clearance where the garage door 'bends' when open.)
(Edit #2: Reading '217's post (below) got me thinking: If clearance with your overhead doors can't be adjusted to work per the above, you might consider installing 'swing open' doors on the garage in place of the 'overhead' type. That might be easier/cheaper than the only other 2 options I can think of at the moment - raising the ceiling like '217 did [if the overhead joists will allow it]....or lowering the floor!) (Actually, there IS a 3rd option as well...moving! :lol)