No, while you spend time in a node (ie, repairing your craft, organizing your crew or weapons, shopping, upgrading, in combat, etc) there is no movement of the rebel fleet. They only move when you make a jump within a system.
In a non-nebula system, jumping through nebula will make the rebel fleet slow dramatically. It's hard to estimate the effect exactly, but at a glance their progress seems to be halved. I do not believe that the effect is as dramatic in nebula-type systems. If you hover over a nebula jump node in the system, you can see this on the tooltip.
There are also certain events that will either speed up or slow down the rebel advance. For instance, if you encounter a rebel scout and fail to destroy it before it charges its FTL drive, you'll find that the next advance of the rebel fleet will be much larger. Likewise, there are certain automated rebel craft that can be hacked to slow the fleet's advance.