(non-cisco specific answer)
Yes, unless you disable it.
The broadcast frames will be sent at the multicast base rate, which is typically low (1 Mbps most of the time), and only every DTIM * beacom interval if there are powersaving stations. And the packet loss rate for those will be quite high.
However, if there are no clients associated to the AP, then the AP will typically be smart and not send them.
200 broadcast packets per second, assuming a 8192 bit packet size and a 1 mbps multicast rate, will just Not Work, since the multicast traffic will be more than 1 mbps, and the AP will typically allocate much less capacity and buffers for broadcast, so the limit is actually much less than 1 mbps.
Anyway, broadcast is so 1990, if you can use multicast instead, and enable MLD/IGMP snooping on the AP, then the AP may be smarter and only deliver the multicast frames if clients actually subscribe to the multicast address. And depending on the client capabilities and the AP configuration, the multicast frames may even be sent as unicast, at higher data rates and with less packet loss.
IPv6 has no broadcast anyway.
So, first of all, TCP is two-way protocol. If there's data travelling one way, you'll have data travelling the other way as well even if only just for the ACKs. You are correct however, that client MAC doesn't change.
The AP association/reassociation/leaving are quite interesting, and it's actually very chatty before AP and Your host assume they have a 'link up' between each other - sometimes it's 'only' four frames being exchanged, but with more security, it's usually whole discussion taking place over wireless. Take a look here for technical description of the process from 802.11 side:
http://www.cisco.com/c/en/us/support/docs/wireless-mobility/wireless-lan-wlan/116493-technote-technology-00.html
Roaming itself became also quite complex process, with natural push to provide seamless mobility for the host roaming. Take a look at 802.11r if You're interested in the details:
https://en.wikipedia.org/wiki/IEEE_802.11r-2008
Best Answer
In infrastructure mode (using a WAP) everything runs through the WAP. For example, your two hosts will be in range of the WAP, but may not be in range of each other. Also, one of the devices may be at such a distance from the WAP as to need a lower rate, which is why broadcast and multicast traffic on Wi-Fi is sent at the lowest rate of the WAP.