The sponsorship for ILR - the undertaking - lasts for 5 years and by signing it you agree that he child will not be a burden on the state i.e. no public funds.
SU 07/12 wrote:I hereby undertake that, if the sponsored person named above is granted leave to enter the UK on a
permanent basis, I shall be responsible for his/her maintenance, accommodation and care in the UK for a
period of five years from the date of their entry to the UK. I am further aware that the sponsored individual
will have no recourse to public funds for five years from the date of their entry to the UK.
This would mean that you would look after the child without claiming public funds. However, a person who is party to an undertaking can claim Child benefit. Therefore, one could argue that this would expand to you claiming child benefit for the said child. Thus with child benefit you can claim tax credits. However, the guidance is not clear.
I suggest you email
SettlementOpsPolicy@homeoffice.gsi.gov.uk and ask them whether a person can claim child benefit for a child that is subject to a SU07/12 undertaking. When you get a response let us know.