Can an appreciating currency lead to inflation?
You are wrong/vague here:

the rupee (INR), is appreciating against, say, the USD, it possibly
means that there is a high demand for the former.

If the rupee becomes more expensive w.r.t. the dollar, demand for the rupee usually decreases, as Indian exports are now more expensive to pay for when measured in dollars, and hence fewer people seek to convert their dollars to rupees to pay for these exports.