As explained much will depend on the varieties you choose but also
the garden orientation and layout meaning which way is North.

Pruning tomato plants may help some but will have to keep at it thruout the season.

This link from the Square Foot Gardening FAQs

may also help What are recommended plant spacings?

Do bush cherry tomato plants also take up 4 sq ft as regular or are they more adaptable to 1 sq ft when planting in raised bed

That depends on if they are full size bush tomato varieties or dwarf tomato varieties.

Frank, if you have the seed packet you can compare the spacing recommended on the packet to the links provided above. I do know I have grown cherry toms that grew quite well.

See much will also depend on your soil, how you care for and water, how much sun, etc. IF your plants are happy they may grow quite well. IF they are not happy you may not have to prune anything.

I do know that in the SQFT books I have read the recommendation is to prune tomato plants to just the main stem. You haven't mentioned if you intend to prune to just the main stem.

HTH

There aren't too many "bush cherry tomato" varieties and they are primarily available only if you grow your own from seed. Tumbling Tom might be available as a transplant and it doesn't need much room at all but it isn't a great tomato to eat either. Most of the common cherry tomato varieties sold as transplants are quite big plants and need lots of room. But if cherries is what you want and assuming you are buying your transplants, your selection is going to be even more limited. So you might just find that one big plant gives you all you need. And in your zone, once the cukes go belly up you will still have time to pull them and stick another tomato plant in that space.

Dave