I don't know if this is the case in LoL's engine, but I suspect it is. In StarCraft 2, the scenario you're describing exists. Let's say you have a worker (SCV) running away from an enemy unit (Zergling) in the early game. You right-click your worker once to send him to safety, and he survives. Alternatively, you panic and spam right-clicks. The pathing is recalculated each time and they add up, and cause a SLIGHT delay, that actually can cause Zerglings to catch up to your worker and click it.
If I'm understanding your question correctly, you're wondering if A+move after move-commanding to a bush, can cause a small enough pathing re-calc that you will slow down a FRACTION of a fraction -- but this fraction is big enough to get you out of cc/initiate range. I suspect the answer is YES, but, so would right-clicking twice (i.e., the pathing recalculation is indepedent of normal move or a-move).
A-moving is generally a good idea though. Smartcasting a ward mid-path is what I tend to do, if possible, even though it WILL delay your movement a bit, in many cases its worth it.
Summary: It is highly-likely, based on the inherent way pathing-calculating engines operate, that every move-command recalculates pathing and adds a slight delay. Each command you stack will set you behind slightly compared to just a single move, but there is no difference between a+move and just move, in terms of "delay."