Is it permissible to consider the 10% pledged to Allah from a sum of money as repayment for part of a debt owed by someone in hardship, and is this method considered fulfilling the pledge to Allah?

If what is meant by "I pledged" is merely an intention, then the vow has not been constituted, and the debtor in hardship must be given respite. It is permissible, and even preferable, to waive the debt for him. There is no harm in giving charity to him or to other poor people.

However, if it was in the form "I covenant with Allah" or "Upon me is the covenant of Allah," then the preponderant opinion is that it is both a vow and an oath if a person commits to it as an act of worship. It is obligatory to fulfill it by giving the vowed amount in charity to the poor and needy, and it is permissible to give it to the poor debtor. It is not permissible to take the money for yourself and count it as part of the debt, for it is a condition of obligatory charity that ownership be transferred to the poor person.