MadPeriot, yes. There are two ways in which this can happen. First, the APs have a table of how many clients are actively associated with the AP, and this table can have a size limit - sometimes small, like on SOHO devices. How many home users have 1,000 clients? Second, 802.11 is a shared medium, and after some not very big number of active users (not idle), it's going to get too slow to be useful. Statistical multiplexing helps with this - not everyone is likely using it at the exact same time - but that only buys you some single-digit factor of oversubscription.
Some enterprise-grade access points (e.g., Cisco) allow you to REDUCE the power of the device and tell the clients to do the same, allowing you to pack more APs closer together, and thus decrease the number of active stations per AP, to deal with heavier volumes.