Not really, no. These probes don't really accelerate by burning fuel; instead they pick up velocity by doing a bunch of gravity assists. The more of these you do, the faster you go, but sometimes you have to coast around the sun for years to align yourself with the next gravity assist, and this gets worse and worse until you hit solar escape velocity. Using this method, your final interstellar velocity will just depend on how many objects you can slingshot around on your final 'kick' out of the solar system. (So, in other words, you can get in the same ballpark as Voyager, but not orders of magnitude faster.)

Here's a video of what it takes "simply" to get out near Jupiter, nevermind out of the solar system. https://www.youtube.com/watch?v=ktrtvCvZb28

The Voyager spacecraft took advantage of a special planetary alignment that won't happen again for over a hundred years.

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Having said that, if by 'spacecraft' you mean something weighing a few grams, the Starshot program might be able to obliterate the Voyager records. https://en.wikipedia.org/wiki/Breakthrough_Starshot