The catalyst at the front of the DPF can which is replaced at the same time as the DPF when you fit a bypass pipe has nothing to do with burning any excess diesel.
There is in fact no excess diesel reaching that part of the exhaust pipe because there is so much oxygen in diesel exhaust gasses that all of the diesel for the regen process is fully burnt by the time it reaches the CAT+DPF device and the gas mixture is already above 600 celsius, the temperaure required for an active regen.
You can confirm this by monitoring with FES or AlfaOBD - when driven normally at 60mph on the flat, the temperature of the first catalyst (called the 'precatalyst') close to the engine is usually at about 300 celsiues. During regeneration it's temperature comfortably exceeds 500 celsius due to the combustion of the diesel added for regeneration taking place within it.
If diesel were injected into the exhaust before the precatalyst and did not burn (as suggested by Timbo) then you would expect to see a *drop* in precatalyst temperature during a regen as a result of the cooling effect created by injecting relatively cold, and evaporating diesel. The significant rise in temperature at the precatalyser clearly indicates that combustion of the diesel used during regen is well under way and needs no additional help.
That combustion continues in the oxygen rich exhaust gasses, through the remainder of the downpipe before reaching it's peak temperature of above 600C by the time it reaches second CAT in the combined CAT+DPF device.
I have pages of colleced data showing this, in the thread 'DPF quick fixes' , viewing it or collecting your own will confirm it.
you can see on the top plot that the temperature of the precatalyst rises significantly when regeneration takes place (in the yellow box), proof that the combustion of the injected diesel is spontaneous and rapid. The second plot down is the DPF temperature which is slightly higher than the precatalyst temperature because not all of the diesel was burnt in the time it took for it to reach the precatalyst.
The remaining unburnt diesel is rapidly burning in the remainder of the downpipe before it reaches the CAT+DFF, which generates a further (approximate)100 degrees celsius of heat. In fact, for a peak DPF temperature of about 720 celsius in the graph above, the precat temperature was very high, at 660 celsius. Obviously, no help is required in generating the temperature needed for regeneration, simply injecting diesel at the right time does an adequate job.
By the time the burning diesel has reached the area of the CAT+DPF device there is no diesel left to burn (no smoke as a result of incomplete combustion either), and there is still an excess of oxygen which then aids with the process of burning off the soot collected in the DPF (there must be oxygen for combustion to take place)
The catalyst in the can with the dpf is a typical Diesel Oxidation Catalyst, it's job is to oxidise carbon monoxide to carbon dioxide, among other things.
Removing the diesel oxidation catalyst is unlikely to cause an MOT failure in the UK because the only emmissions test done during the current MOT for diesels is a smoke density test. But, it is important to know what the devices are and how they work.
If carbon monoxide testing of diesels becomes part of a future MOT test then things might not be so rosy. Because it is a true catalyst, removing the second CAT in the DPF assembly has the effect of allowing high levels of carbon monoxide to reach the tailpipe.