I doubt it. The largest capacity SD card I can find is 1 TB. Which weights around ~250 mg. With a data rate of 200GBps 25 1 TB SD cards are transmitted every second, 6.25 grams per second. From a quick google it takes astronauts anywhere from 4 hours to 3 days to get to the ISS so let's take the low number, 4 hours.
4 hours * 6.25 grams per second is 90 kilograms. I doubt anyone can just carry around 90 kilograms in their pockets. Let alone when going to space.
I think the correct calculation is that 1 TB SD card can hold 40s of 200Gbps traffic (1TB = 8Tb = 8000Gb; slightly more if these were actually TiB/Gib). So, 4h of 200Gbps traffic would be recorded on 4*60*60 / 40 = 360 cards. That would weigh 360 * 0.25g = 90g.
Even with 3 days, that's 18*90g = 1620g = 1.62kg, well within rocket carrying capacity.
However, arranging 360 SD cards by hand in the right order is much harder than relying on TCP SEQ numbers, though.
Also, the satelites are not likely to be in geostationary orbit - so those 200Gbps are only being achieved for 5 minutes when they are in reception (possibly once or twice a day):
> With data rates of 200 gigabits per second, a satellite could transmit more than 2 terabytes of data—roughly as much as 1,000 high-definition movies—in a single 5-minute pass over a ground station.
I think your calculations are off by a factor of 8 - network speeds are quoted in bits, rather than bytes. Apologies if I've misunderstood your comment though.
4 hours * 6.25 grams per second is 90 kilograms. I doubt anyone can just carry around 90 kilograms in their pockets. Let alone when going to space.