I have a ZYNQ-7000 XC7Z030
I have no pullups or downs on the VMODE pins.
Can I still configure the device with JTAG.
If so, can I boot the processor from QSPI or SDRAM after that?
JTAG should always work, unless disabled by the efuse configuration bits. But the uSD or QSPI boot won't work unless you have the MODE bits set correctly.