Yes, time and space are, to some extents, "linked". I'm not sure exactly what you mean by "shrink" in this question. It is true that the expansion not only makes distant galaxies recede at velocities proportional to their distances, but also makes their time run at a slower pace, as observed by us.
This general relativistic time dilation is observed all the time, e.g. in supernova lightcurves which show how their brightness of supernovae decline with time after the explosion. The farther away a galaxy is, the slower it is obseved to decline.
This does not cause their redshift; rather, both effects are caused by the same phenomenon, namely expansion. But both effects add to diminish the flux that we receive from distant sources. The wavelength of light that we receive from a galaxy is "stretched" by a factor $(1+z)$, where $z$ is called "it's redshift" and is given by the size of the Universe when the light was emitted, relative to the size it has now. General relativity predicts, and observations confirm, that time is dilated by the same factor, $(1+z)$.
That is, the flux we receive is diminished by a factor $(1+z)^2$ more than the usual inverse square law predicts — one factor for the less energy per photon (due to the redshift), and one factor for the smaller number of photons emitted per time interval (due to the galaxy's time interval taking longer than our time interval).
All of this is true irrespective of the rate of the expansion; in particular whether the rate is accelerating.