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She can but payment will depend on the type of ESA she is receiving.
If she is only receiving ESA(CB) then the CA is classed as an overlapping benefit and will not normally be paid as the ESA(CB) amount is higher.
If she is receiving ESA(IR) in whole or in part then the CA will be paid but treated as income so her ESA(IR) will be reduced by a similar amount, however, a Carers Premium of just under £35 per week will be added to her ESA(IR).
If she is not receiving ESA(IR) then she may be eligible. ESA(IR) is dependant on your household income, your savings and assets, and any hours that your partner works. See
Asset rule for ESA(IR) 24 hour work rule for ESA(IR) Gordon