The answer is "It Depends, you didn't provide enough information".
Put yourself in the shoes of the optimizer.
You see this query that does a SELECT *. C is most likely not the only column in the table, let's say you have both columns A and B as well.
That means that an index seek on C will require a lookup operation for each row to bring back A and B from the table.
Now it boils down to the cost - If you have 1M rows, and IF the optimizer can realize that your query will return 1% = 10,000 rows. That means the cost of using the index is performing the index seek, getting 10K rows, and then performing 10K lookups to bring back columns A and B.
Unfortunately, MySQL does not maintain histograms like some other engines, but only the density vector... So it may estimate that ~10% of the rows will be returned, and with that info the estimated cost will be much higher.
The alternative, is to scan 1M rows and filter 'on the fly' without using the index.
Which is cheaper? I don't know - that depends on the size of the table. If A and B are both BOOLEAN columns which take up very little space, it might think that it will be cheaper to scan the table. If A and B are huge BLOBS, it most likely will increase the estimated cost.
BTW.. if instead of using * (which I assume you only gave as an example), you would list only the minimal set of columns that you need, let's say A and C, then a composite index on (C,A) will always be the cheapest choice as you just saved yourself the lookups..