No, even if light had an infinite velocity in all inertial frames, it would not necessarily imply that time is absolute. The constancy or variability of the speed of light is not directly related to the concept of time being absolute or relative.
The theory of relativity, developed by Albert Einstein, challenges the notion of absolute time and introduces the concept of time dilation. According to the theory, time is not absolute but depends on the relative motion and gravitational fields between observers.
In special relativity, which applies to situations without gravity, the speed of light is considered constant in all inertial frames. However, this constancy of the speed of light does not lead to the conclusion of absolute time. Instead, it leads to the observation that time can dilate or contract depending on the relative motion of observers. This effect is known as time dilation, and it has been experimentally verified in numerous experiments.
In general relativity, which incorporates gravity, the concept of time dilation is further extended. Gravitational fields can also cause time dilation, meaning that the rate at which time passes can vary depending on the strength of the gravitational field.
So, even if light were to have an infinite velocity, the principles of relativity would still apply, and time would continue to be relative rather than absolute. The constancy of the speed of light does not have a direct impact on the relativity of time.