2017 iMac with Mac mini start up drive

No.

If you get or have a Mac mini, then you need a Display, Keyboard and Mouse or Trackpad.

Please remember iMacs are computers, they are not external displays for other devices.

I don't know whether it's relevant to your question but you can boot your iMac from an external USB or Thunderbolt connected SSD or HDD. Dead easy and breathes new life into your old machine.