Faith should always be supported by at least some evidence -- evidence stands behind the "confidence" portion of one's belief. If the relic is not the shroud of Jesus, then it's a lovely work of art. If it is, then it points to the historical truth of his death and resurrection. Such evidence would not convince those who are hard-core against the existence of Jesus, or the essential message of his passion, but it would provide further evidence for many's faith.
In short, one's faith doesn't stand or fall on a single relic, like the Shroud -- Faith is built upon the Gospel of Jesus Christ as contained in Scripture and proclaimed by the Church -- however, it is never "bad" to have other physical evidences for one's faith than the written word.
Holy Sheet!!!
Faith and evidence, by definition, are mutually exclusive. Evidence proves fact, not faith. Faith depends upon belief alone. The certainty of that which is unseen, unproven. It is the depth of ones faith that is important, not the evidence.
I have no problem with those who have their faith reinforced by relics, as long as there is understanding that relics can be fashioned by man to deceive the faithful as well.
Whether the Shroud of Turin is authentic or fake, the knowledge of either condition should not increase or diminish the depth of the faithful.