You can get a frenulum piercing as long as you have enough tissue available. Unlike the labial (lip) frenula piercings, this one doesn't pose any risk to your teeth or gums, but it can still rub against the bottom of your tongue and the floor of your mouth, causing irritation. The simple fact that it's almost irresistible to "play" with foreign objects in your mouth, the pulling and tugging on the piercing with your tongue can make it really sore. Especially during the first couple of weeks, you've got to try to resist the urge to play with it.
The lingual frenulum can be pierced successfully with either a curved barbell or a CBR (usually 16 gauge), but a barbell used for initial piercing would have to be longer in order to accommodate swelling during the first few weeks of healing. If this is the case, see if your piercer offers a free jewelry change once the swelling has receded. Many professional shops include this jewelry change in the initial price of the piercing, because wearing the correct jewelry size is extremely important for a successful and healthy piercing.
Healing time for all oral piercings are relatively short as long as you don't play with it, have good oral hygiene and don't smoke. If needed, you should be healed enough for a jewelry change in 4 weeks.