Since this discussion has devolved into a technical argument of the where space starts I think it's about time for all involved to move on.
I wanna circle back just a second (and I hope y'all will give me this one indulgence...) - you are correct, the technical boundary between the Earth's Atmosphere and Space isn't even really the issue here.
The issue is, does Luke have on-screen experience flying spacecraft before he Mary Sues his way into becoming a hero with a next to impossible lucky shot?
The answer is, resoundingly, no. Now, Luke brags about his amazing piloting skills, but we never see this in action prior to his amazing X Wing show.
Likewise, I can brag about my amazing singing voice, but I can't hum a tune in a box.
Luke's Skyhopper is, apparently, non-functional during ANH due to Luke's wreckless piloting skills as well. But that's not said in the script, so take that with a grain of salt..
But let's say Luke piloting the Skyhopper is like Anakin piloting a Pod Racer, but more whining and less terrible kid acting. Let's say he's literally the best creature to ever exist that has ever piloted a Skyhopper.
Is the Skyhopper a spacecraft?
Technical definitions aside, there are two primary factors that are going to define an actual space craft apart from a fancy plane. The first is the planet's atmosphere (friction, lift, etc.). At the max altitude of 300km ("Low Earth Orbit"), while still in Earth atmosphere, the air is so thin it is virtually not a factor. Although piloting a craft into that altitude would require a totally different skill set than boosting a ship out the shuttlebay doors, one could argue *that* actually takes more skill. However, it is a totally different set of skills. Most importantly, we don't really know *how* the Skyhopper works (since it's not shown on-screen - but there could be some out of the many expanded universe canon that details it). To achieve LEO (On Earth, of course.), it requires a speed of roughly 28,000 km/hour. A quick search shows Luke's Skyhopper with a max speed of 1,200km/hr. Not only is this speed well under the required speed for getting into orbit, it seems quite low for routinely reaching the max altitude claimed - regardless, the maximum speed of the craft is far to low to maintain an orbit, implying the name of a "Skyhopper" is just that, a craft that doesn't maintain these crazy altitudes for any significant amount of time, likely "hopping" from a landing pad to another.
Why does a ship need to maintain such speeds in order to maintain an orbital flight path at 300km? The second of the two factors that defines a space craft from a fancy aircraft - gravity.
In low earth orbit, gravity is about 9/10ths that of normal Earth gravity - fairly indistinguishable from planetary gravity. Now, I'm no expert, but I think it's safe to say there is a significant difference in piloting a craft in the gravitational field of a planet versus being in space, especially when gravity can so wildly fluctuate based on surrouding celestial bodies. Remember, gravity doesn't just 'end' in space.
So, the effect of the atmosphere on the Skyhopper is negotiable with the details we have, but the effects of gravity are significant.
Is the Skyhopper a spacecraft?
Ima gonna go with my first answer. Luke has no on-screen experience flying spacecraft until we see him jump in an X Wing and save the day.