Yes, they have the same meaning, though I would say that "As time goes by" sounds a bit more old-fashioned/formal than "In time", which to me is more neutral.

The simple answer is yes, they are pretty much interchangeable. However, when in doubt, use "over time" because it is shorter, plainer, simpler, and more common. "As time goes by" has a kind of poetic or nostalgic feeling to it, a feeling that you are talking about something important, about a long sweep of time, about patterns of social change, or growth and experience, or aging. "Over time, the filter in the air conditioner will get dirty and should be removed and cleaned." "As time goes by, I find that my birthdays seem less and less important." The movie, "Casablanca," makes effective use of a song that illustrates this feeling: "You must remember this, a kiss is still a kiss, a sigh is still a sigh-- The fundamental things apply, as time goes by; And when two lovers woo, they still say 'I love you,' on that you can rely, No matter what the future brings, as time goes by." https://youtu.be/1_a57ZNlU6o?t=79