No, it could not be considered a tactical draw, in my opinion. The Union Army didn't have to totally destroy the Confederate army, drive them from the field, or severely demoralize them to achieve victory. If that's the criteria you're using, then the Battle of Chancellorsville is also a tactical draw. The Union Army was not destroyed. Nor were they driven from the field. It was easily winnable for the Union right up until Hooker decided it was not. However, most of his core commanders wanted to stay. And the Union soldiers were not demoralized. What most had trouble with was all the sacrifices they were making and the death surrounding them, only to have the lead general quit the field the moment the battle turned against them. Furthermore, Lee lambasted his generals for not crossing the river in pursuit of Hooker with wording that was very similar to Lincoln's unsent letter to Meade. Except Lee was a whole lot less polite and more than willing to speak his mind in front of everyone.
And actually what Gary Gallagher said, which Allen Guelzo backed up, is that Confederate morale did plummet at first, but then recovered. Gallagher said the very same thing about the first Battle of Bull Run. Union morale plummeted, but soon recovered. So, good luck selling that battle as a tactical draw.
The difference between strategic and tactical is that strategic is the long term plan and tactical is the short term actions to get to that goal. In other words, it's long term goals versus short term goals.
Hence, it was not a strategic victory for the Union. There was no long term plan that they had which involved Lee marching into Pennsylvania, raiding a bunch of towns, and threatening Washington D.C. It was a tactical victory for the Union because they achieved their short term goals: Find Lee's army, protect the Capitol, and drive the invaders back across the river and out of the north. Abraham Lincoln would probably say it was a strategic defeat, because the long term goal was to destroy Lee's army and win the war. But, in actuality, it really had very little strategic significance for the Union, especially in comparison to Vicksburg. The strategic defeat was at the Battle of Chancellorsville, and Meade was essentially left doing damage control. Even if it wasn't part of their strategic plan, leaving a Rebel Army to run amuck through the Pennsylvania countryside is obviously not going to help their chances for ultimate victory. Had Meade destroyed Lee's army, though, then it would have been both a tactical and strategic victory for the Union.
It was both a strategic and tactical defeat for the Confederacy. Lee did not achieve his long term goals, which was to win the war by forcing the Union to accept a negotiated peace. And he failed to achieve it, because he failed in his short term goals, which were raiding supplies, hurting northern morale by raiding and/or a decisive defeat of the Union Army on northern soil, and taking the fighting out of war torn Virginia. Admittedly, though, one could argue that it was a partial tactical victory. Lee did conduct raids. And I suppose you could say he took the fighting out of Virginia, if you happen to think one battle was much of a respite for the state. Regardless, it was all nullified due to the outcome of the battle.
As far as the first day of the battle, that was a tactical win for the Confederacy, but a strategic win for the Union Army. Reynolds and Buford knew they couldn't defeat Lee's army with only the troops they had. All they were trying to do is hold the high ground until the rest of the army got there, which they achieved.
Bringing the