Many trailers attach via a hitch on the rear axle of the bicycle. Since bike share bikes use proprietary fittings to reduce theft, it would not be possible to install one of these on a bike-share bike.
The trailers you are asking about appear to attach to a seat post. Bike share bikes always have adjustable (but not removable) seat posts. You should have no problem adjusting the post and installing one of these seats.
You may find it's not worth your effort attaching and detaching a trailer when you're likely to be only using the bike for a half hour at a time.