NOT if the bootloader was just flashed.
If the bootloader was just flashed, the rest of memory would be erased (contains 0xFFFF) If the bootloader were to try to "start the sketch", it would jump into that string of 0xFFFF instructions (which is some non-jump instruction), and execute them one after another until ... the program counter reached the bootloader again.
Similarly, symptoms like yours can occur if you have not programmed the "start at bootloader" fuse. The AVR starts at 0, executes 0xFFFF instructions until it reaches the bootloader, and then runs the bootloader. Unless there is a real program at 0.
I'm also remembering some incompatibility between bootloaders and JTAG. But I haven't used JTAG, so it's not something I know about for sure.