The use of the word 'network' to describe a number of computerized devices connected together is a relatively recent sense. And there are fine distinctions in the use of the word between professionals (electrical engineers, computer scientists, etc.) and the general public.
In everyday use, it's common to use "on" when describing the end-user devices (printers, computers, smart phones) or resources available to end-users (file shares, servers)
Is that printer on the network?
Are you on WiFi right now?
We're installing cabling today so you can get on the network from the conference room.
We have a big shared disk on the network where we keep all the training videos.
A professional would use 'in' when describing the devices that are used to construct the network - routers, switches, cabling, etc. - which are usually invisible to the end-user.
We use Brand X switches in our network.
Did you specify proxy services and address hiding in the network as part of the security plan?
In your example, 'on' is appropriate and will probably be understood by most people. If you're writing for a professional audience, you may need to add some extra clarification.