@ 9600 baud continuous mode one can send about 2000 longs (binary = 4 bytes) of 32 bits enough to switch on/off 64000 leds Or 64 leds 1000 times.
in text mode one need max 11 bytes to send one long(+ separator) so that makes 32000 leds.
phrased more seriously:
How many LEDS's are there?
How often do the need to be refreshed?