Sort of. But not the same system.
Here's a photo of the directions the two Voyager probes (and a couple Pioneers) are traveling:
They're also not traveling in a flat plane, as this page says:
Voyager 1 has crossed into the heliosheath and is leaving the solar system, rising above the ecliptic plane at an angle of about 35 degrees at a rate of about 520 million kilometers (about 320 million miles) a year. (Voyager 1 entered interstellar space on August 25, 2012.) Voyager 2 is also headed out of the solar system, diving below the ecliptic plane at an angle of about 48 degrees and a rate of about 470 million kilometers (about 290 million miles) a year.
I was able to find some good information here. Voyager 1 is headed towards Gliese 445. However, it will be 1.6 light-years away at its closest approach - not exactly close by! It will reach that star, 17.6 light-years away, in 40,000 years.
Voyager 2 will go by Ross 248, a red dwarf currently 10 light-years away. The craft will take 40,000 years to get there. 256,000 years later, Voyager 2 will come within 4.3 light-years of Sirius.
The probes will have absolutely no power by that time.
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