Hi, I just bought this cycle carrier and have fitted it to a Peugot 206.
To answer your question, no, you can't open the boot.
The rack is hung over the rear of the car using a dumb-bell type arrangement - the dumb-bells are inside the hatch of the car and the straps fall outside. With the boot closed, the weight of the rack will then pull the straps taught and tighten the dumb-bells against the seal/hatchback of the car. If you were to try to open the boot, this may pull the dumb-bells out of alignment and you would not be able to close the boot again. Also the lower straps connect to the chasis of the car (or tow hitch or similar) so that the rack is tightly mounted from top and bottom - these straps would have to be slackened to open the boot.
The instructions expressly say not to open the boot with the rack mounted.
If however you still are interested in the product, I would say that the rack can be quickly unmounted and re-mounted (possibly <10mins?) if you wished to access the boot. It is only a matter of slackening a few straps.