It's not just possible its certain!
Here is a shot of one of the rakes on Flickr. Although this one is dated April 1965 such sighta were quite frequently seen in the area during 1966 and 1967. Depending on how long it took to clear out Salisbury MPD, where they were all assembled at the end, some could even have run in early 1968.
But these of course were special workings, not ordinary passenger or greight runs. Andy K has posted that freight work continued into August 1966,citing Colin Maggs' book. Perso nally I would like to see some hard evidence of that as I have never heard of it before, and don't recall the railway press mentioning it either. And it is well documented that there were no servicing facilities on the WT after the end of 1965.
All that said, of course, there was perhaps more unofficial autonomy on the railway in the 60s than there is today. Whilst watering facilities may not have been officially available, it is quite possible that enterprising staff with a hose pipe could top up a tender with water, and a Black 5 or 8F could have run Saltley to Bristol and back on a tenderful of coal.