Using steady state for Transient Initialization
 

How will the convergence of steady state simulation of a problem will affect its transient simulation if used for initialization?

Too vague.

In general, if you plan to use the same turbulence modeling approach in both steady and unsteady (laminar/DNS or RANS/URANS) then, if the steady solution makes any sense, you don't need the unsteady one.

If using RANS to initialize LES/DNS, you probably want almost converged mass fluxes and a good enough distribution of the turbulent quantities used to initialize the fluctuations

Paolo addressed the main issues.

Just to add that if you have a steady flow problem and you run a transient formulation starting from the initial steady numerical solution, you should find the code stops immediately as it reached the correct solution.