No, it is unlikely to be true.
Here is one version of the story
There’s a story about how Dr. Albert Einstein was traveling to Universities in his car , delivering lectures on his theory of relativity. During one journey, the driver remarked ” Dr. Einstein, I have heard you deliver that lecture about 30 times. I know it by heart and bet I could give it myself.”
You can find versions of this story adapted for several different famous and non-famous people.
There is a tendency for the subject of old stories to be reassigned to more recently notable persons. A storyteller might rework an amusing anecdote to associate it with someone his audience is more likely to know of. It is probable that more readers of this story are aware of who Albert Einstein was than are aware of who Jacob Kranz was.
According to Snopes
This story has long been part of the canon of Jewish folklore, usually framed as a tale about the envious manservant of a wise rabbi who has been invited to address a gathering of elders in a distant town.
You can easily find old tales of the preacher of Dubno
For example: God Laughed, Friedman & Friedman, 2014:
That evening, as he drove the wise rabbi to his lodging, the coachman sat upon his box and wondered what it might feel like to be so honored and revered as the Preacher of Dubno. What must it feel like to ride into town to cheers and happiness? What would it feel like to earn the love and admiration of everyone, near and far?
Often the preacher is identified as a Jacob Kranz (example)
Once upon a time there lived a man named Jacob Kranz who was known as the Preacher of Dubno, famed far and wide for his wisdom and his parables.
He traveled from town to town teaching ...
... as the coachman drove the wise rabbi to his lodgings, he wondered what it would be like to be as respected as the Preacher of Dubno ...
The origins may lie with Jacob ben Wolf Kranz of Dubno 1740-1804 - predating Albert Einstein 1879-1955
As described in One a Day, Bloch, 1987
1804 - Rabbi Jacob Kranz, a famous itinerant preacher known as the Dubner Maggid, dies at the age of sixty-four. The Maggid's unrivalled eloquence, combined with a creative genius for homespun parables, spread his reputation throughout the Jewish world. He used parables to elucidate biblical texts and to drive home important messages. His parables were frequently interlaced with subtle humor ...
Of course, none of this proves that Einstein and someone who drove him did not repeat this act. It is however, less likely that a driver (even one not employed as such) would match Einstein's rather well-known appearance and also be able to give a convincing speech on the sort of subjects that would be expected of Einstein.
In his later life, Einstein is described as being something of a loner, who preferred to stay out of the spotlight and stay near Princeton. It seems unlikely that he employed a driver to carry him to numerous speaking engagements.
It is arguably more plausible that a devout and long-serving servant of a famous itinerant preacher, in the years before photography, could initially deceive an audience who had never before seen the preacher.