No, Race, it is you who is stretching "bound" into "wrapped".
Here is the definition of "bound"
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bound
Bind \Bind\, v. t. [imp. Bound; p. p. Bound, formerly Bounden; p. pr. & vb. n. Binding.] [AS. bindan, perfect tense band, bundon, p. p. bunden; akin to D. & G. binden, Dan. binde, Sw. & Icel. binda, Goth. bindan, Skr. bandh (for bhandh) to bind, cf. Gr. ? (for ?) cable, and L. offendix. [root]90.]
1. To tie, or confine with a cord, band, ligature, chain, etc.; to fetter; to make fast; as, to bind grain in bundles; to bind a prisoner.
2. To confine, restrain, or hold by physical force or influence of any kind; as, attraction binds the planets to the sun; frost binds the earth, or the streams.
He bindeth the floods from overflowing. --Job xxviii. 11.
Whom Satan hath bound, lo, these eighteen years. --Luke xiii. 16.
3. To cover, as with a bandage; to bandage or dress; -- sometimes with up; as, to bind up a wound.
4. To make fast ( a thing) about or upon something, as by tying; to encircle with something; as, to bind a belt about one; to bind a compress upon a part.
5. To prevent or restrain from customary or natural action; as, certain drugs bind the bowels.
6. To protect or strengthen by a band or binding, as the edge of a carpet or garment.
7. To sew or fasten together, and inclose in a cover; as, to bind a book.
8. Fig.: To oblige, restrain, or hold, by authority, law, duty, promise, vow, affection, or other moral tie; as, to bind the conscience; to bind by kindness; bound by affection; commerce binds nations to each other.
Who made our laws to bind us, not himself. --Milton.
9. (Law) (a) To bring (any one) under definite legal obligations; esp. under the obligation of a bond or covenant. --Abbott. (b) To place under legal obligation to serve; to indenture; as, to bind an apprentice; -- sometimes with out; as, bound out to service.
To bind over, to put under bonds to do something, as to appear at court, to keep the peace, etc.
To bind to, to contract; as, to bind one's self to a wife.
To bind up in, to cause to be wholly engrossed with; to absorb in.
Syn: To fetter; tie; fasten; restrain; restrict; oblige.
Source: Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
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Well, Race, what do we find. The accepted usage of "bound" has nine definitions in this meaning - and only #3 comes even close to your interpretation while number 1,2,4,5, and 6 plus the list of synonyms seem to support MY interpretation.
The Amplified Bible renders the relevant passage thusly:
7But the burial napkin (kerchief) which had been around Jesus' head, was not lying with the other linen cloths, but was [still] [1] rolled up (wrapped round and round) in a place by itself.
This is taken from the most original source material and translated with alternative usages of the Greek words included as well. Note the description of the Sudarium... "burial napkin (kerchief)" and the description of its condition after the resurrection: "[still] rolled up (wrapped round and round)". These give clear indication that it was rolled when it was on Jesus and still rolled afterwards. If the Greek meaning was that it was "rolled up (wrapped round and round)" then it could not have been a covering for the face... it was a binding.
The Sudarium of Oviedo