Assuming you are referring to IB's VWAP algo: not 100% sure, but I believe an empty end time will produce the same result as specifying 4:00pm. I do know if you specify an end time of, say, 11am, it will usually finish by that time or earlier, unless it's an illiquid stock or it has a 5-cent tick size.
The Allow Past End Time setting just means if the algo fails to get done within the specified time frame (happens more often in illiquid names, obviously), it will continue to try for the rest of the day. If you have it unchecked, the order is cancelled immediately upon end time.
In general, there is really no reason to leave the end time empty. You either want the order spread throughout the whole day or you want it done more quickly. My assumption is that empty = 4pm, but that could be wrong.
The answer is no. But if you don't believe me, why don't you just contact IB?
Pretty simple. If you have an end time, it will try to get done by that time. If it fails and you have the keep order active box checked, it will try to get done ASAP (while obeying your size and aggressivity specs). If you leave it blank -- again, no idea why you would do that -- it probably treats that as 4pm, and so would try to space out the orders from start time until 4pm.
Liquidity matters because some stocks are easier to trade than others, esp. when telling the algo to be passive. So all else being equal, illiquid stocks are less likely get filled within the times specified.