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No, for several reasons.
The first and most important is that Sirius B and Sirius A have, as seen from Earth, a minimum angular separation of 3 arcseconds. They never eclipse each other.
Also, Sirius B is much smaller than Sirius A, and they're at about the same distance from Earth, It's too small to block more than a miniscule fraction of light from Sirius A. A more accurate description of what would be seen from Earth if it could actually line up with A would be a "transit", not an eclipse.
Finally, periastron occured in 1994. The two stars have actually been moving further apart since. Since the period is about 50 years, the next time they're close together won't be for another three decades, and certainly not this year.
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