The bootloader reserves some SRAM for its own operation, and disallows access to this area. Reading out the rest of the SRAM shouldn't be a problem.
For example:
$ stm32flash -S 0x20000200 /dev/ttyUSB0 -r /tmp/sramout
stm32flash 0.7
http://stm32flash.sourceforge.net/Interface serial_posix: 57600 8E1
Version : 0x22
Option 1 : 0x00
Option 2 : 0x00
Device ID : 0x0410 (STM32F10xxx Medium-density)
- RAM : Up to 20KiB (512b reserved by bootloader)
- Flash : Up to 128KiB (size first sector: 4x1024)
- Option bytes : 16b
- System memory : 2KiB
Memory read
Read address 0x20005000 (100.00%) Done.