Can I use my blender for food processing the ingredients in my Gazpacho?
The main difference between a food processor and a blender is its shape and how the food is mixed while it is being "cut up".

In a blender, it relies on the funneling action of liquid to mix the food around. Otherwise only the bottom gets blended while the top stays solid. 

Food processors usually have a flat bottom and have a mechanism to turn the food as it cuts it up. This results in evenly chopped food.

If you want the gazpacho to end up completely smooth, then the blender will definitely work in this application as it will be liquid enough to get the funnel action going to mix the food around. Keep it mind it would be a good idea to start blending the vegetables with high water content such as tomato and onion first to create a liquid "base" for the other vegetables.

IF you want coarse chunks for the vegetables, it is slightly trickier but still possible to use a blender. You need to work in smaller "batches" and use the pulse functionality instead of just blending. If the batch is too big, you end up with overblended mush on the bottom and unblended chunks on top.