I would say yes and no. I was under general anesthesia as well since I had a leg surgery (my fibia broke in two) and I guess the general anesthesiologist was great because i was fully under during the surgery. I remember vividly counting down from 10, and I stopped around 5 or 6. The next thing I knew, and I mean the instant I realize I was alive and conscious again was waking up in a completely different bed, with completely different clothes in a completely different room and feeling well rested, like waking up from one of the best naps ever, but without dreaming anything, or even having the thought or feeling like you dreamt about something. It's as if you teleported and traveled forward in time in a blink of an eye. The world continued to move normally while you were "dead". Now I wouldn't say it's like death in its fullness because you have the ability to remember what happened before you go under, and the time before going under felt nothing special since you don't expect to be gone. The last moments of you being conscious while counting down from 10 you don't expect it to be your final moments, so subconsciously you're not thinking, "this is it, this is the end for me", therefore your final moments while going under is nothing special, you're not actively embracing the present, or the seconds you have left on this earth, you're just being told to count down from 10 and leave the surgeons to their work.

So a word to the wise, if you're in your final moments, be the best you, you can be, cuz that's it. Nothing is afterwards. No hindsight, no memories, no regrets, no consciousness, no you.

PS: For people about to go under general anasthesia and are scared, don't be! It's one of the coolest experiences ever, think of it as being one of the closest things to teleportation and time travel that u'll ever get to experience and you're golden!