Thanks for posting!
While we don’t have the Precision 5510 in our test lab, we do have a XPS 15 that comes with a 130 watt power adapter. When using our triple dock with this XPS 15 system, when the system boots it displays a ‘warning’ that the a lower power adapter has been connected but does in fact charge the system (Windows reported the system was charging at the same rate as the original adapter). I would expect the Precision to behave similarly based on customer reports.
To your question about plugging in the original power adapter while connected to the dock, Dell does not appear to publish specific details about how the system is intended to perform when two power adapters are connected at the same time. As a quick test, I connected the original power adapter while the XPS 15 was connected to the triple dock and Windows reported it was charging at the same rate as it has when connected to the dock alone.
Please let us know if you have any additional questions!