The number I’m getting is about 2 photons/minute per steradian; a steradian has solid area 1m^2 at 1m away. With fully dilated pupils (8mmish) you get an area of pi x 2 x r^2 = 50mm^2, which gives us a rate of about .15 photons/day.
So… Maybe. If you’re very lucky. It’d be interesting to do the same math for a room temp object to see if you’re above the noise floor at all or if this is completely impossible, but I should go do my actual job instead of letting myself get nerdsniped by this.
Warning! Madness this way lies.
I'm thinking back to the movie Real Genius during one of the montage scenes where they're cramming for finals in a common area when one student just stands up from his material and starts screaming in madness before fleeing. Everyone else, just behaves as if this is normal as someone takes the now vacant place at the table.
That guy screaming in madness? That's me after just thinking of doing the math without even grabbing a pencil.
Otherwise one can create a machine concentrating all the thermal radiation of one black object at temperature T1, onto another perfectly white object also at T1 with a tiny black hole, heat up the second and then violate the second law of thermodynamics.
Keyword for further Googling: etendue
...in a vacuum, of course!
The angular diameter of a human pupil (~5 mm) at a distance of ~2 m is about 0.2 degrees, taking the small angle approximation. So the area of the pupil is maybe 0.04 square degrees, or around one millionth of a full solid angle (~41,000 square degrees).
Assuming a spherical isotropically radiating human, the probability of hitting a pupil from any distance is thus pretty unlikely.