IANAL, but based on the EFF's page on warrant canaries, it seems like they can, in a way. They can state any legal processes they have not been involved in, for basically any period of time, though EFF recommends several months between any such kind of report. The easiest thing is for them to issue, say, quarterly transparency reports and saying "For this past quarter we have received no XYZ".
Some services have a daily canary (like https://proxy.sh/canary), but we don't know whether they could be forced to sign a new canary even after they've been served an NSL.
