Yes, you can have additional license servers with HP QTP installed on them and not be out of compliance with HP. HP QTP is considered by HP Class 1 software. So you are authorized to have the following additional licnese servers.

Class 1

For Class 1 products, HP provides Non-Production licenses at No Charge for perpetual licenses only. You may receive up to six (6) Non-Production licenses for each production license acquired:

• one (1) for a use on a Hot Standby System,
• one (1) for use on a Cold Standby System,
• one (1) for use on a Development System and
• three (3) for use on a Test System.

HP's definition of Hot Standby System, Cold Standby System, Development System, Test System, and Non-Production

• ''Hot Standby System'' means a non-production system which is up and running, ready to take over from the production system if the production system breaks down or needs to be taken out of service.
• ''Cold Standby System'' means a standby non-production system which is NOT up and running. If the production system breaks down, or needs to be taken out of service, Licensee is required to switch on and start the Cold Standby System in order to take over for the production system.
• ''Development System'' means a non-production development system which has a software product installed and is to be used for developing software product add-on applications.
• ''Test System'' means a non-production test system which has a software product installed and is to be used for a) software product migration testing, or b) software product pre-production staging.
• ''Development and Test Systems'' means a Development System and a Test System.

HP provides no charge Non-Production licenses for all Enterprise Security, Information Management, IT Management (previously called Hybrid & Cloud) and Vertica products, except those identified as Class 2 and Class 3 products below.

Class 1 Non-Production licenses will be provided to customers upon request as described below.

Process for requesting Class 1 and Class 4 Non-Production licenses

If you have an HP order number, you should contact one of the HP Licensing Centers listed at www.hp.com/software/licensing to request Non-Production licenses. Please be prepared to provide: original HP order number used for production licenses and products/quantities for the Non-Production request.
If you obtained licenses from HP acquired companies (and do not have HP order numbers), you should submit a support case for a non-technical license request through www.hp.com/go/hpsoftwaresupport.