Can my company's IT department remotely install the Find My app on our iPads?

If your iPad is being managed by your company, they can add pretty much anything they want.

Note that "Find My" is an app that comes pre-installed on your iPad. So, unless it was deleted at some point, they wouldn't need to add it.

If your iPad is "supervised" or centrally managed by an MDM platform - as is common with Business/Enterprise owned devices - you would be wise to assume that anything and everything that you do is potentially monitored by, and is visible to, your employer. When centrally managed, all aspects of your device are potentially under full control.

If you are concerned for your privacy, you would be best advised to keep your work and private activities entirely separate - and use different devices for each.

You're very welcome.