Yep, try them and let us know, people often uses such type in order to save money, time. There's no problem will occur during growing in tea bags, however let us know if anything happens.
I believe we will have to take the content out and then use that for the plants and such.
Or else, you could probably look for biodegradable bags for tea bags as well
Flavoured tea usually contains chemical substance as a purpose to enhance the tea taste (some use flower extract and others use real flower). Those naturalist / organic gardener might need to know about this. Some tea bags are also made of nylon. Most paper tea bag also contains chloride/bleach to whiten the colour of the bag.
You can use used teabags, used tea leaves, and used ground coffee in your soil. These items provide nutrition to the plants. However, make sure you rinse properly before using, especially if you have used sugar in your tea.