Instead of copying the number, you can copy the entire URL (also known as the web address) of the plant in question.
Take a look at this plant:
Lambsquarters (Chenopodium album)
The url looks like this:
http;//garden.org/plants/view/80986/Lambsquarters-Chenopodium-album/
(I replaced the colon with a semicolon so the url wouldn't be converted by the ATP system.)
You can put that in the multi-plant tag field instead of the plant ID and it'll work, too. In fact, that's usually how I do it because it's more convenient to just copy and paste the web address instead of going down the page to get the plant ID.