Well, kind of. The time dimension is a bit tricky, though -- in Minkowsky space, a common way to think about spacetime, it is hyperbolic in relation to the other dimensions. In a nutshell, this means that distance is not the square root of the sum of the squares of the distances in specific dimensions, but rather of the difference. This makes it especially tricky to visualise. (I do recommend you check out this series by minutephysics, he does a great job at making it intuitive)

My analogy, therefore, doesn't translate directly to spacetime, but it does provide a very simple 2d explanation for why straight things can act curved (even in 4d).