If it's actually your server that actually attack another server, they will shutdown your server and give you a warning. They will let you boot in their recovery os that let you access your file system but if your server does it again, they terminate your account.
No, it's not. They have a proper anti-ddos solution in place for attacks from outside of their network[1].
[1] https://www.ovh.co.uk/anti-ddos/ddos-attack-management.xml
This is an internal attack, which requires different mitigation measures, and is seen less often in the wild (compromising 500 servers from a specific provider is more difficult than 500 random servers on the internet, and you're pretty much guaranteed that the provider will deactivate most of them after the first attack), so I guess their protection systems aren't as developped against it.
But if you receive DDOS attack to your server from outside, they can defend you using network resources.