Can I use Vimeo Pro as a Secure Video Server?

Yes you can certainly use Vimeo Pro as a secure Video server for the VOD application that you are doing for your client. We have recently designed an MVP for one of our client which also uses Vimeo Pro as a video server. And its working good for them.You can authenticate Vimeo Pro account in your application and provide an Upload Video window to your client from within the application.Once approved by Vimeo you will receive a token Id corresponding to that video and then can stream it from your frontend. Few addition settings can help further, In the setting for individual video in Vimeo Pro dashboard under "Privacy" tab you can define Who can watch this video? mark it as "Hide this video from Vimeo" and also Where can this video be embedded? as "Only on sites I choose" and give your URL address where you want it to be streamed.You can also implement any open source player in the application that you are developing and by this can have complete control over what is getting displayed in the front-end.Although Vimeo also provide customization of its player. See if it suffice your purpose.Also, with bit of efforts you can completely white-labeled the application,  have your own chosen payment gateway implemented with no commission deducted by Vimeo and can hide the Vimeo from "src" displayed by Inspect Element and View Source, if required.Thanks

By default I believe Vimeo is secure, only downside is Vimeo keeps your customers and you do not have access to them, they also take payment in there own name and take a commission. You can try UscreenTV http://www.uscreen.tv they take no commission and charge a simple platform fee per month, you can fully sell the videos securely and even setup a subscription website like Netflix or Hulu. Best of Luck!