Hello and welcome!
No you cannot connect a SIO device easily to an ST or STE.
There are probably solutions to connect through the serial port but you cannot readily procure such equipment and software. I faintly remember some solution from 87 or 88 with a custom software. But I am unaware about the features or which magazine contained the article. Likely to be ST Magazin or 68000er here in Germany.
The ST series uses the ACSI bus to connect mass storage. E.q. SD card readers are the UltraSatan or CosmosEX devices.
Simon Sunnyboy/Paradize - http://paradize.atari.org/Stay cool, stay Atari!
1x2600jr, 1x1040STFm, 1x1040STE 4MB+TOS2.06+SatanDisk, 1xF030 14MB+FPU+NetUS-Bee