The answer is absolutely yes. DO IT! If you do have trouble with the height just go back down. As somebody said it's not about how trained you are, the affect is individual and you have to get up there to see how it specifically affects you and the adjust to the situation. Needless to say your heart must be healthy doing this.
I did a badly planned and equipped little trek for one day in 2013. I went from sea level (Puerto de la Cruz) to about 2,500 m and back again after some beer and water in Las Cañadas del Teide. It was dark when I got back after this 60k walk. As you can see I didn't go straight at all and had to battle with dogs and thirst since I had too little water with me. But besides some ill tempered dogs and really dumb path choices there was great trails and small roads all the way up up and it was truly epic. Some of the descent was pretty much jogging down in a straight line through the the terrain, which was a bit gnarly, until I hit the roads further down. I didn't want to end up on the mountain in the dark.
I had trainers and shorts, t-shirt, sunglasses, sun screen and a hoodie in a little backpack. Food wise I had two candy bars, an apple and 1 liter of water with me... as I said badly planned, time and food wise. The clothes and trainers worked really well.
I could really feel the height (heavy in the head/head ache, swollen hands, breathing like pregnant hippopotamus) but other than feeling tired with a "few" blisters on my feet I felt freaking great when I got back!
With better planning and maybe some advise from any of you of the straightest/fastest path up, or if someone wants to join, I'd like to see if I can do Teide (view point at 3 500) from sea level and back again in one day. I'm 46, healthy and in OK shape and I have done a few really average marathons done in the past. I'll be in Puerto de la Cruz Nov 23rd to 30th 2014.
You can see the plot from my trek. The spike in the end is from a 2 km car ride I got from a local since it was getting dark and I had no clue which way to go except down ;)