Can I use Both inputs at the same time on the Bass Block 800?

When using both inputs, they are connected by resistors at a similar level, but the impedance of each instrument will load the other. If you have an active bass, this won't be a problem. A passive bass (in the passive input) will lose a little volume to the synth input, but you should be able to increase the Gain to make up, and then balance the synth level. using its volume control.

If using a bass synth on the Active input it will load the Passive input with about 30K, which will reduce the treble response out of the P-bass, and the volume control will cut back more quickly from full, compared to the normal 1M input when using just the Passive input.

 You could avoid these effects by using the XLR Line Input for your synth, which usually has plenty of output volume. This input bypasses the pre-amp tone controls and our trick limiting system, but the synth presumably has the sound you want already, and a reasonably well-controlled peak volume (unlike the percussive nature of a string bass). Plus, this frees you to adjust the pre-amp controls to get the sound you want for the P-bass. The Master will still control the volume of both instruments, but the other controls on the preamp will only affect the P-bass.