Massive spatial modulation aided multiple-input multiple-output (SM-MIMO) systems have recently been proposed as a novel combination of spatial modulation (SM) and of conventional massive MIMO, where the base station (BS) is equipped with a large number of antennas and simultaneously serves multiple user equipment (UE) that employ SM for their uplink transmission. Since the massive SM-MIMO concept combines the benefits of both the SM and massive MIMO techniques, it has recently attracted substantial research interest. In this paper, we study the achievable uplink spectral efficiency (SE) of a multi-cell massive SM-MIMO system, and derive closed-form expressions to asymptotically lower-bound the SE yielded by two linear BS combining schemes, including maximum ratio (MR) combining and zero forcing (ZF) combining, when a sufficiently large number of BS antennas are equipped. The derivation takes into account the impact of transmitter spatial correlations, of imperfect channel estimations, of user-specific power controls and of different pilot reuse factors. The proposed asymptotic bounds are shown to be tight, even when the scale of BS antennas is limited. The new SE results facilitate a system-level investigation of the optimal number of uplink transmit antennas (TAs) $N$ with respect to SE maximization. Explicitly, we provide theoretical insights on the SE of massive SM-MIMO systems. Furthermore, we demonstrate that massive SM-MIMO systems are capable of outperforming the SE of conventional massive MIMOs relying on single-TA UEs.