No, every plan (including Trial) includes unlimited notifications.
However, please note the API rate limit of 800 requests per minute for the Pushy API.
Note: This doesn't mean you are limited to sending just 800 notifications per minute. You can target multiple devices in the same API request which will only count towards 1 request of the 800 requests per minute capacity. You can do this either by specifying multiple device tokens in the same request or sending to a Pub/Sub topic.