No. Installing third-party apps on the Magento Commerce (Cloud) servers is not allowed. You must host such applications on external servers.
Terms of service agreement
The Magento Enterprise Cloud Edition Terms of Service Agreement states the following in its Article 18:
Customer agrees that Magento and the Service will not be used to host other third-party software applications that are not directly dependent on the Software.
Being a Cloud solution, Magento takes full responsibility for the security of your server. To guarantee high security, we only allow hosting the Magento Commerce application on the dedicated Cloud server.
As a PCI-certified Level 1 Solution Provider, Magento Commerce (Cloud) must follow the PCI Data Security Standard and make sure to:
... Develop and maintain secure systems and applications
(Magento Approach to PCI Compliance
Requirement 6, Maintain a Vulnerability Management Program)
Since Magento cannot guarantee the PCI compliance of third-party applications, installing such apps on the Cloud servers is not allowed.
Hint: Use Magento Marketplace extensions for better integrations
To improve integration of your Magento Commerce (Cloud) application with the third-party solutions hosted on external servers, we encourage you to use the Magento Marketplace extensions that might suit your purpose.