Not in essence, but in form - yes.
Godel: mathematics reflecting on mathematics itself.
Hegel: consciousness is thought reflecting on thought itself.
Heidegger: Being is that Being that can reflect on Being.
The essence of mathematics is different from that of consciousness; but the above remark shows that a certain perspective brings out similarities in form that hadn't been noted uptil then.
Consider - mathematics in essence is timeless; Consciousness is in time - one cannot reflect on Consciousness without also reflecting on time and in time - one thinks of Heideggers Being & Time - perhaps a better title would have been Being in Time or Time in Being; Can the two be torn apart? Considered alone? Being Alone? Time Alone? Is that not an error of abstraction? Time is an essential difference between Mathematics & Consciousness or between Mathematics & Being.
(one should note that Hegels formulation has entered popular consciousness in that human beings are uniquely self-conscious, meaning conscious of the conscious-self. Heidegger refines it).