No. A cunning American moviemaker, Bernard Rose, was the one who "invented" this hypothesis in 1995 and there's no reason to take him seriously. There's not the slightest trace of a proof that Beethoven and his sister-in-law were interested in each other. On the contrary. From the moment they met their relationship was a hostile one and later on the two began to hate each other. Serious biographers shrug their shoulders about Rose's hypothesis. Yet he was not the first who frankly showed this dissident opinion. As far as I know a Dutchman, one Harke de Roos, was the first who postulated a hypothesis about a love affair between Beethoven and Johanna, though not with Johanna in the role of Immortal Beloved. If we may believe De Roos Johanna and Beethoven had a short affair in winter 1805/6. The result: Karl, who was born in September 1806. This hypothesis is not completely impossible, though also not very likely, to say the least. On the contrary.
See:
Rose, Bernard and J. Ellison. Immortal Beloved. (London, 1995).
De Roos, Harke. Beetgenomen door Beethoven. (Katwijk aan Zee, the Netherlands, 1987).