Hypothetically yes, it will last a while - if a sealant is used in a tube and the tire subsequently gets a puncture, you must remove the penetrating object or it will flex in the tire, continually un-sealing the hole and shredding the tube.
If you believe you completely removed whatever caused the puncture and the sealant plugged the hole and you were able to continue your ride, that's great!
Some steps to further make sure the sealant will hold for future use:
- If significant sealant was lost during the puncture and you have a removable valve core, add more sealant.
- If you are truly concerned if the tube will stay plugged you can add glitter through the valve core. This helps plug holes, especially depending on the type of sealant you are using.
- Reattach the valve core and inflate the tire.
- Spin the wheel to mimic the motion of rolling down the road.
Given enough time, most sealants cease to be active and should be cleaned out; if they solidify, they unbalance the tire with useless weight concentrated in a single spot. On a tire with an inner tube, including a tubular, you’ll need to remove the sealant through the valve, which requires removing the valve core, and ideally rinsing and sucking it out. That is a lot of work if it is a tube in a clincher wheel. So you could always deflate the tire, remove the tube and insert a brand new tube and repeat the steps listed above.