I have been running a tubeless setup on my bicycle and have picked up a number of foreign objects (e.g. thorns and glass shards) in the tyres. The sealant is doing its job and I am not losing significant amounts of air from any of the punctures. Given that the tyre is holding air is there any value in removing the objects?
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.
Tires flex a bit every time make a revolution. Tires are flexible, most foreign objects are not, and the latex in sealant is flexible. If there is a thorn it will move slightly every time it goes around, and if it comes in contact with another part of the round it will move substantially, and eventually cause the tire to weep sealant and air in mostly small amounts.
I'd rather see the latex there than the thorn, it will flex with the tire and keep the hole sealed. That being said it's a pain to remove all of the thorns, so I'd get most of them out. Bigger objects I would remove as soon as possible.
tubeless bike tire plug.