The simple answer is “YES”, with conditions. If your furniture is located inside of your house, it is extremely rare that termites survive in furniture inside your house. Termites must have soil to wood contact in order to survive. If your house is one of those historic houses with wooden floor touching the ground directly and your furniture is placed right on to it, well, there could be a chance, but I highly doubt this would be anyone’s case.
Now, if your furniture is located outside, let’s say your backyard, the story is different. Your furniture is in direct danger of termite invasion! But you can save your outdoor furniture from termites easily. Termites are big enough to be spotted with human eyes. If you see any signs of termites, just move your furniture to somewhere safe where it doesn’t touch the ground.
There’s a myth about cedar furniture. Many argue that cedar is resistant to termites because of the oil and resin in cedar, but experts say that they’ve seen enough to confirm that termites DO eat cedar. Termite eats outdoor cedar furniture and fencing when they are in direct contact with ground plus they have not been moved at all for many many years.
In any case, if you find something’s wrong with your furniture inside, it is probably something other than termites.