The 20,000+ employee corporation where I finished my career prohibited copy/paste on many of their emails and web pages, as well as forbidding the forwarding of company email. Don’t know how well their practices and policies worked for them, but it was their system to do with as they pleased. Just one of the many reasons I disliked working at large corporations.
And, you know, those IT and security professionals were rarely amused about anything. 
Security folks are the absolute worst 
As a follow up to this, I can imagine these events
You use your own uncertified iPad (computer) for company work. The device is stolen. The company information is made public and the company traces back to the reason.You will be held liable.
You use your own iPad (computer) for company work. You are given a certification stamp to use a certain package of software on that device. You use some other software as well to work with the company information. The information leaks out from the other software (perhaps the device is stolen as above and the other software is not as secure or perhaps the other software has a security breach). The company information is made public and the company traces back to the reason. You will be held liable.
As others have said, you would do well to become better informed about the details on the IT policies for using your own computer and software to work on company information. What are the absolute bounds and their consequences? You can give them your device ID as a way for them to give you an unlock key on your device. This may only clear you to use their certified software on your device. Or better said, it may still leave you on the short end of the stick if you use some other “uncertified” software and subsequently do something that is a violation.
—
JJW
Another point is that companies themselves are liable for data loss. Therefore they have a legal duty to protect it. Here in the uk organisations have been fined where employees have lost data. Since GDPR this is a hot topic.
I help run a charity and won’t allow any data on personal devices unless we have permission to remotely wipe in case of loss or theft. We also stipulates the complexity of passwords used to access their own devices. This is not draconian, but a simple fact of needing to secure personal and special data as we are liable for its security.
Copy/paste might be worse because of this:
Personally, while there may not be any harm in giving the serial number, I would never give my personal device in that situation. I payed for it, I decide what I can do and can’t. I had a similar situation in my previous workplace.
I would first make the case for why you need it and have the company buy you an iPad. keep your personal stuff personal.
And if it does get lost of stolen, you can’t be held responsible because you weren’t following the “rules”.
Thanks all. I won’t give them the serial number. Luckily I’m not dealing with nuclear launch codes or the secret formula to Coca-Cola, mostly organizing curriculum which is actually more powerful when it’s shared. There are elements of my work (PHI) that cannot be shared and those are pretty locked down in proprietary systems, already.
I understand it is a balancing act between not using your own stuff because the Company should buy what you need. And making your every day working a bit easier - by using your own stuff. That was the position I was in - it really made life nicer each day to be able to pull out my iPad and work on that for certain things. But they wanted to lock it down, wipe the contents and set it up with thier way or thinking. A bridge way too far for me. Maybe your situation is a bit less intrusive. Only you can decide where to find the balance.
But I am a big believer in asking the company to supply the stuff that makes working better. Even if they don’t understand why. The worse they can say is no.
In a different part of my job, they do issue us iPhone 8+'s. The thing is so locked down all I can do is make calls, use a proprietary program and use a bunch of apps IT thought would be useful but really aren’t. The password is of dal{nkq23093lkd-23-type and touchID is disabled. Forget about adding useful apps or using shortcuts. A Siri enabled “remind me to do xyz in 20 minutes” would be lovely. But alas, no.
The work supplied devices are too locked down to be useful.
A common statement, I am guessing.