No. Eight slots remain but the stated conservative bound needs nine before extra margin: seven arrivals during service plus two reserved in flight. Trigger at occupancy 7 or earlier, reduce the gap or add buffering.
Common trap: Giving a generic fix without identifying the boundary and unmet obligation in this example.
The receiver had no capacity when a character needed to be retained. Measure arrival rate, frame size, FIFO/holding-register capacity, trigger level, worst-case interrupt or DMA service latency and flow-control reaction distance. Possible repairs include earlier service, more buffering, effective flow control or a lower offered rate. Baud mismatch usually presents as framing/parity/data errors and should be checked separately from a reported overrun flag.
Common trap: Blaming the external device.