Yes.
If the BBC had given it proper money, publicity and changed its time slot back to Saturday then it absolutely could have got back some viewers.
Following this, if for season 28 they'd cast an 8th Doctor who was a reasonably big name to attract publicity, got rid of JNT and brought in a new producer (Leonard Nimoy was interested at that point.) DW could have entered a new golden age.
Remember that the end of the Troughton era saw the biggest decline in viewers there has ever been for the show.
3 million at one point, and that's in a time with just 2 channels, where its still supported by the BBC and given the best time slot. People only don't comment on that being a dark age for the show because the 70s saw it recover. Had it been allowed to, then the 90s could have been a new golden age like the 70s.
And sorry but people who say the BBC were being fair in 1989 are just letting their hatred of 80s Who get in the way.
The BBC made a calculated effort to kill the series in the 80s. That's a fact. Yes its true that there are things wrong with parts of 80s Who, but come on here!
They slashed its budget, gave it no publicity, took it off the air for 18 months when its viewers were nowhere near low enough to justify cancellation, fired its leading man, forced JNT, a producer who didn't want to be there to stay on, put it up against Coronation Street (and at one point a qualifier for England for the World Cup.)
They also raised the prices for the show abroad to the point where no one could buy them.
See here.
Really the fact that it last 5 years under those conditions is a testament to its appeal, and the strength of a lot of 80s Who too.
Having said all of that, I'm actually not sorry that it ended in 1989. It had to end some time, and that was a good ending. Had it gone on into the 90s, the Fitzroy Crowd would have taken it over as they were waiting in the wings, and then their shit would be fully connected to True Who, as opposed to just one of many alternate sequels.