Yes, even in an all-glass tank, none of the glass panels are actually contacting each other. This tank is built differently; it is a metal frame with the panels glued individually to the frame, so the larger gap you discovered is not surprising You can and should remove as much silicone as possible but without damaging the thin layer that actually holds the glass to the frame. That layer would be pretty difficult for you to access in this tank so you're pretty safe.
The only catch here is that, since the gap along the seams is larger, the bead you apply will need to be large/wide enough to span the entire gap and bond securely to the glass on either side. It will also need to be thick enough to cover the gap all the way across and remain solid despite the fact that it is not actually adhering to the old silicone within that gap.
You are going to use several times as much silicone to do this job as you would if it were a standard all-glass tank where the new bead can be very small and thin. Buy lots; you simply cannot take the chance of running out midway. It must be done all at the same time or else all your work is useless and you would need to start again from scratch.
You should also probably accept that this won't be the sleek sexy little seam we typically expect to see in the corners of professionally-constructed all-glass tanks. But this tank can definitely be waterproof again. Make it so!