Most people here would tell you no, don't worry about it. The process of racking will release some CO2 from the beer that will form a protective blanket right above the surface of the beer. The truth is that some oxygen will still make it through, but probably not enough to matter.
I often use both 5 and 6 gal carboys for secondaries all the time with 5 gal batches, and had no problems with either. I only have one 6.5 gal carboy, but it gets reserved as a primary fermenter since that extra headspace is very handy for containing a high krausen.