First up, the answer depends on what type of termites are creating the problem. If they are drywoods, then maybe knocking things down will kill them, but if these are subterranean termites then definitely not. Drywoods live in small colonies, usually in individual pieces of timber, so a thoughtful demolition may effectively remove active colonies. Subterraneans, don't, they like to spread out through the structure and will have paths to ground (for water).  They will just go to ground at the first vibrations and come back up later to resume the attack somewhere else.

The really odd thing about termite swarms is that it is the one time when cooperation goes out the window.  Its every termite for his or her self.

In some parts of the world, particularly parts of Africa and Asia, termites will quickly attack and kill transplanted trees and plants.  They attack the roots.  In the past, some very heavy doses of scary pesticides have been used to help the plants get established.  The attacks seem to drop off once the plants have been in for a few months. Keeping the plants well-watered all the time can make a big difference as water-stressed plants are more readily attacked.

Around the world, ants are the main predators of termites.  When you see termite soldiers, most of the funny-shaped jaws or pointy or blocky heads are effective adaptations against ants.  When termites fly, lots get eaten before they can create a safe nest.  This makes life very hard for termites, but usually not so hard as to kill them all off.

Keeping termites in the garden largely means leaving them alone.  Keeping those termites out of you house can be harder.  For the subterranean pest forms, particularly some species of Coptotermes and Reticulitermes, it is probably better not to take the risk.  To be sure, you need to know what species you have and how much of a risk they are in your area.