Yes tomatoes and cucumbers can be grown together and they do well when they are grown together.
Cucumbers and Tomatoes are companion plants and both tomatoes and cucumber plants are beneficial to each other when they are growing.
I grow tomatoes alongside cucumbers every garden season and they do well.
However you do not want to grow potatoes alongside cucumbers or tomatoes because they don't do well with each other.
But you can grow tomatoes and cucumbers together and they will do just fine.
In fact I find that since I started growing cucumbers and tomatoes together that they both grow much better than they did when grown separate from each other.