The bill would have to be paid down below £500 for it not to have a negative impact on the application. Simply agreeing to a payment plan wouldn't be enough.
eta, I'm not sure what effect a bill of less than £500 would have on the application as we always suggest people pay in full before applying.
I agree it's good advise to speak with an immigration lawyer. But I don't think it's necessary to pay down the debt to less than £500, based on the guidelines provided for data sharing between the NHS and Home Office.
Quoting below from the link:
The NHS cannot notify the Home Office of outstanding debts in any of the following circumstances:
-The NHS must not tell the Home Office about a debt owed by an EEA national, her/his family member or a non-EEA national who has derived residence rights in the UK because they are the carer of a British or EU citizen (known as Zambrano carers).
-The NHS must not tell the Home Office of outstanding debts if you are challenging the decision to charge you, for example, where there is a dispute about your immigration status or whether you are ordinarily resident.
-The NHS must not tell the Home Office if you have an agreed payment plan in place and you are sticking to it.-The NHS must not inform the Home Office of outstanding debts where the debt has been cancelled.
-In Northern Ireland, the guidance states that the NHS must not inform the Home Office of a debt, if it has been written off. The England guidance is silent on this point.
And also refering to point# 14b (pages 5-6) of below:
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/507694/Overseas_chargeable_patients_2016.pdf