  We theoretically investigate the possibility of excitonic condensation in a
system of two graphene monolayers separated by an insulator, in which electrons
and holes in the layers are induced by external gates. In contrast to the
recent studies of this system, we take into account the screening of the
interlayer Coulomb interaction by the carriers in the layers, and this
drastically changes the result. Due to a large number of electron species in
the system (two projections of spin, two valleys, and two layers) and to the
suppression of backscattering in graphene, the maximum possible strength of the
screened Coulomb interaction appears to be quite small making the weak-coupling
treatment applicable. We calculate the mean-field transition temperature for a
clean system and demonstrate that its highest possible value
$T_c^\text{max}\sim 10^{-7}\epsilon_F\lesssim 1 \text{mK}$ is extremely small
($\epsilon_F$ is the Fermi energy). In addition, any sufficiently short-range
disorder with the scattering time $\tau \lesssim \hbar /T_c^\text{max}$ would
suppress the condensate completely. Our findings renders experimental
observation of excitonic condensation in the above setup improbable even at
very low temperatures.
