Will model resolution have an effect on model spin-up time?
Without spin-up time, our initial conditions would be blank or generic. 

I guess the simple answer is "NO" spin-up time is not really affected by the resolution, unless the model resolution changes are so great that it takes much longer for diffusion / advection between cells to flush out. Though that wouldn't explain a 5 year change in spin up time unless you made drastic changes to a model with very large time steps. Increased model resolution could theoretically increase the necessary spin-up time by a small amount, if the changes in resolution were very large and the time steps used were coarse.   However, in a reputable research setting the spin up time is chosen based on how long (in model time) it takes for things to get to an acceptable initial condition, and changes in resolution are usually not so extreme.  

Complexities in the model can increase desirable spin-up time if they have long time-horizons before an acceptable initial condition is achieved.  The spin-up time you choose for your model will influence the degree to which the initial conditions actually represent a realistic distribution of numerics across all parameters, assuming the model is adequately developed.