I think that what Francisco did would not violate the oath. The actual oath that had to be sworn to join the strikers is described in Part III Chapter One as follows:
I SWEAR BY MY LIFE AND MY LOVE OF IT THAT I WILL NEVER LIVE FOR
THE SAKE OF ANOTHER MAN, NOR ASK ANOTHER MAN TO LIVE FOR MINE.
This does not seem to forbid all work; rather it forbids a certain mindset. At the end of that chapter, John Galt elaborates on what the oath actually meant in practical terms:
"We had no rules of any kind," said Galt, "except one. When a man took our
oath, it meant a single commitment: not to work in his own profession, not to
give to the world the benefit of his mind. Each of us carried it out in any
manner he chose. Those who had money, retired to live on their savings. Those
who had to work, took the lowest jobs they could find. Some of us had been
famous; others — like that young brakeman of yours, whom Halley discovered— were
stopped by us before they had set out to get tortured. But we did not give up
our minds or the work we loved. Each of us continued in his real profession,
in whatever manner and spare time he could manage — but he did it secretly, for
his own sole benefit, giving nothing to men, sharing nothing. We were
scattered all over the country, as the outcasts we had always been, only now
we accepted our parts with conscious intention.
Again, this seems to indicate that it was not work per se that was forbidden, but specifically work that was done to help the world. Similarly, when Galt intends to go back to work in the world for the last time in Chapter Two he explains that it is not a violation of the oath because his particular reasons for working were valid:
"If I go back," said Galt, "it won't be for our work. It will be to win
the only thing I want from the world for myself, now that the work is done.
I've taken nothing from the world and I've wanted nothing. But there's one
thing which it's still holding and which is mine and which I won't let it
have. No, I don't intend to break my oath, I won't deal with the looters, I
won't be of any value or help to anyone out there, neither to looters nor
neutrals — nor scabs. If I go, it won't be for anyone's sake but mine — and I
don't think I'm risking my life, but if I am — well, I'm now free to risk it."
Therefore, we can perhaps say that Francisco was able to do the same thing. He didn't take the job as the furnace foreman in order to be productive for the world; He took it to advance his own agenda by enabling Rearden to join the strike.