If you value your Arduino and all and sundry connected to it BY ANY MEANS POSSIBLE IF you intend to load it to the Max... Keep the PSU output (Mains Operated) to 7V5. There are any number of "Switcher" type Mains PSU's that are and can be had for cheap... The easiest way to tell them apart is the Switcher types are about 1/3 the weight of a transformer type and the Switchers are "Usually" (I've not found one that wasn't) spot on as to the marked voltage being accurate form 0 to full load current.
If you are going to use batteries into the DCin jack by all means keep that voltage to the equivalent of 5 Alkaline cells in series. All of this is to avoid overheating that regulator... data sheet says 165C... Keep it below 90C for a long and happy life.
Bob