Here's a "Jolly Coachmen" text that appears to antedate Brand's by a few years. It appears among a number of WW2 Army Air Corps songs collected by former fighter pilot Bill Getz.

Besides that context, it seems unlikely that Brand's "jolly mother" would turn into "fruitful mother" (instead of the other way round).
                  
                  
                LANDLORD, FILL THE FLOWING BOWL

Three jolly coachmen sat in an English tavern.
Three jolly coachmen sat in an English tavern.
There they decided that; there they decided that,
There they decided that they'd have another flagon.

Chorus:

Oh, Landlord, fill the flowing bowl
Until it doth run over.
Oh, Landlord, fill the flowing bowl
Until it doth run over.
For tonight we'll merry merry be;
For tonight we'll merry merry be;
For tonight we'll merry merry be;
Tomorrow we'll be sober.

Now the man who drinks light ale and goes to bed quite sober;
Now the man that drinks light ale and goes to be quite sober.
Fades as the lilly [sic] fades, fades as the lilly fades;
Fades as the lilly fades. He'll die before October.

Chorus.

But the man who drinks stout ale, and goes to be quite mellow;
But the man who drinks stout ale and goes to be quite mellow;
Lives as he ought to live; lives as he ought to live;
Lives as he ought to live. He'll die a jolly fellow.

Chorus.

Now the maid who steals a kiss and runs to tell her mother;
Now the maid who steals a kiss and runs to tell her mother;
Does a very foolish thing; does a very foolish thing;
Does a very foolish thing. She'll never get another.

Chorus.

But the maid who steals a kiss and stays to get another;
But the maid who steals a kiss and stays to get another;
Is a boon to all mankind; is a boon to all mankind;
Is a boon to all mankind; she'll be a fruitful mother!

Chorus.