Briefly, in principle yes, however in practice the procedure is non-trivial. In principle, the carrier concentration can be obtained from the integration over momentum and frequency of the one-particle spectral function, measured by ARPES. The practical problem arises from the fact that real systems are described by many bands, resulting in the frequency range to perform measurements being impractically too wide. In practice, for measuring the carrier concentration one can rely on optical measurements and use of the Kubo sum rule [1,2] regarding the optical conductivity. 

[1] R Kubo, J. Phys. Soc. Jpn 12, 570 (1957).

[2] M Tinkham, Introduction to Superconductivity, 2nd edition (McGraw-Hill, New York, 1996), p. 88.