Time constant of parallel RC circuit
If you apply Norton's or Thevenin's equivalent circuit theory, it'll be apparent that a series RC circuit is no different to a parallel one. The time constant is the same.
In your circuit, R2203, C2202 form a high pass filter. One presumes in that circuit to prevent 'nuisance operation' of the current sense.
Again, in answer to your question, apply Norton/Thevenin circuit analysis. You'll see that the 1.87 ohms is insignificant and the RC time constant of the sense circuit is 1k.10u or 10 milliseconds.