Path integral Monte Carlo calculations have been performed to investigate the microscopic structure and thermodynamic properties of the Ak . He-N (Ak=Li, Na, K,N less than or equal to 300) clusters at T=0.5 K. Absorption spectra which correspond to the P-2 <-- S-2 transitions of alkali atoms are also calculated within a pairwise additive model, which employs diatomic Ak-He potential energy curves. The size dependences of the cluster structure and absorption spectra that show the influence of the helium cluster environment are examined in detail. It is found that alkali atoms are trapped in a dimple on the helium cluster's surface and that, from the asymptotic behavior, the Ak . He-300 cluster, at least semiquantitatively, mimics the local structure of experimentally produced large helium clusters in the vicinity of alkali atoms. We have successfully reproduced the overall shapes of the spectra and explained their features from a static and structural point of view. The positions, relative intensities, and line widths of the absorption maxima are calculated to be in moderate agreement with experiments [F. Stienkemeier, J. Higgins, C. Callegari, S. I. Kanorsky, W. E. Ernst, and G. Scoles, Z. Phys. D 38, 253 (1996)].