Should I remove foreign objects from my tyres if I'm running tubeless?
In general, I would recommend removing thorns and other debris even if the sealant is holding. Tubeless sealant is typically latex based and designed to adhere to rubber, not glass or wood fibers. As mentioned in The Benefits of Going Tubeless the sealant could fail to seal around a foreign object and leak air until it is removed. While not immediately obvious a poor seal could allow a slow leak which will require reinflating the tyre more frequently. The usual argument against removing thorns is that you will be reopening the puncture and losing air as the sealant plugs the hole again, however given you are free to do this at your leisure you should be able to reinflate the tyre at the same time.

The major reason to remove foreign objects instead of letting them build up is in case you get a puncture so severe you need to use a tube. As DWGKNZ mentions in their answer to How do you fix a puncture on tubeless tires? if you leave thorns in the tyre you will need to remove them anyway when putting a tube in and it'd certainly be more comfortable to remove the majority at home instead of on the side of a trail.