My salad and herb containers all contain worms- not added by me I might add, but they're near a worm bin so they may be escapees. If you've any compost, which may not be fully broken down in your boxes, I'd definitely add a few worm cocoons and when they hatch they'll get to work releasing nutrients from your soil.(If they hatch in the boxes they're less likely to flee). But if you plan to add artificial fertilizer, don't add worms, it's not very good for them.

Would a bit of organic fertilizer be OK? Such as Tomato Tone?

I don't know the brand, but it should be as long as it's well diluted.