If you choose tissue cultured plants then there's a 100% guarantee the plants you receive will be snail and pest free.
If you're buying any other type of a plant there is a chance you may receive some hitchhikers. Whilst we keep all our plants hydroponically like the commercial growers (outside of water), this doesn't guarantee there won't be any pests on them. It's unlikely of course but a possibility.
Worms / slugs / greenfly
This is very occasional but as all plants are grown without the use of pesticides, only natural and safe remedies are used. In the greenhouses, you might be surprised to hear they use toads to eat slugs and worms and they also use biological pests to deal with green/black fly. Occasionally worms are found in pots often surprising the customer.
However, if you find any pests, don't fret - it's very natural. A quick rinse under tap water before adding to the aquarium or placing the plants in a bucket of water for 24 hours solves the problem. Any pests that do end up in your tank become fish food. They are totally harmless in your aquarium to all live stock.