Yes, we do have some restrictions. 

With shared hosting plans:

• more than 50 emails per hour on our Personal hosting plan.
• more than 100 emails per hour on our Business hosting plan.
• more than 200 emails per hour on our Professional hosting plan.
• more than 400 emails per hour on our Ultimate and Reseller hosting plans and with all Hosting PRO plans.

VPS and Dedicated Servers have strict limits on sending out emails, as we do not allow to send mass emails without agreement. Sending mass emails may damage IP addresses, so Bacloud should be sure, that IP addresses will not be used to send spam.