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In simple terms being awarded a benefit always consist of two checks, eligibility for the benefit and entitlement to payment.
Being in receipt of DLA Care (or PIP) means that you are entitled to ESA, where someone with DLA would not. It actually only qualifies you for the WRAG as you are classed as having Limited Capability for Work, you would still need to be assessed for the SG.
Whether you are entitled to payment will depend on whether you qualify for ESA(CB) or ESA(IR), the latter will take into account your student funding as income, so payment will depend on how much you receive. The following fact sheet explains how the DWP account for this in regard to any ESA payment.
www.disabilityrightsuk.org/how-we-can-he...d-questions-students Gordon