Yes! There is no doubt that a 25-06 will do the job.
On a whim last year I bought a 257 WBY Vangard. I have been getting outstanding results with Nosler 110gr AB's. I recomend you give that load a try.
This year I did a bang flop @ 385 yds (lasered) on a 4pt mule deer using my 270 Win, 130gr Sierra SBT @ 2950 fps. Nothing special, but a very accurate load. Based upon the post-mortum analysis of the wound channel, I would have been just as well served with my 6mm Rem and it's Sierra 100gr SBT @ 3000 fps load.
With very little effort you should be able to get 3150 fps using a Nosler 110gr AB out of that 25-06 and this is why I think it will "do the deed" out past 600 yds.