graduate admissions - Should I mention about my governmental-funded PhD scholarship which I don't want to use

This might sound odd, yet here is my story. I was lucky to get governmental scholarship (GSch) for 4-5 years of PhD to study abroad. But It requires student to work as Assistant Professor in a relatively smaller university in my homeland for 8-10 years afterwards. Which I would not like myself bound to after my PhD.

This is an advantage for sure to get admission in a top university. But by myself (without using GSch), I might also get funded by TA/RA. In that case, I wouldn't use GSch.

Should I mention GSch in the first contact with PIs or in PhD applications (i.e. in SOP)? I am asking this because once I inform them about GSch, it is unlikely to get TA/RA funds even though I deserve. I also don't want to lose the chance of PhD in a top university, I use GSch if needed. So there is a trade-off.

I can think of three possibility:

1 - Mentioning the GSch in the first contact, hoping that they will promise funding anyway if they this I deserve.

2 - Mentioning it in the first contact as it is a possibility.

3 - Sending another email and mention it if they reject me because of lack of funding (Would they say it is lack of funding?).

P.S. : I am planning to apply mostly to positions in U.S.

P.S.2 : Sorry for bad English level, edits are welcome.

Edit : If I decide not to get back to my country, I have to pay scholarship in 5 years with ~50% interest.

Answer

This is a tricky situation. If you mention the scholarship without explaining your reservations, then it might help you get admitted, but you'll be admitted with the understanding that you'll use this scholarship. Not having to pay for you is exactly why it could give you an advantage, so the department would probably be upset to learn that you didn't plan to use it. It would feel like a form of cheating, and you might face pressure (such as withholding other sources of funding on the grounds that you had this scholarship available).

If you don't mention it, then you don't have to use it but it won't help you.

Sadly, there's not much room in between these possibilities. You could try mentioning it but explaining your reservations about using the scholarship. However, this isn't likely to help your chances (nobody cares about the scholarship if you won't actually use it), and it might create an awkward situation if they try to convince you to use it.

I also don't want to lose the chance of PhD in a top university, I use GSch if needed.

This is a judgment call you'll have to make regarding when to reveal the scholarship.

Sending another email and mention it if they reject me because of lack of funding (Would they say it is lack of funding?).

Probably not. At least in my experience, rejected candidates are not given a specific explanation. On the other hand, you might end up on a waiting list, where you may be admitted if a suitable spot opens up (for example, if someone else turns down an offer). That could be a time when revealing the scholarship would help your chances, if you are willing to use it.