Not really. The similarity of the shibaru and shiboru verbs is probably not accidental. One refers to tying or binding, the other to wringing, squeezing. And in fact, shibori is something we might call tie-dying, a literal translation of which would therefore like to go to shibari.
There are many Japanese words with similar or identical pronunciation, but the difference is quite clear when written in Kanji (or given some context). 縛り and 絞り don't look particularly similar, they just share the 糸 radical.
Shibori (絞り, also 搾り) is, first and foremost, simply the noun form of the verb shiboru (絞る, 搾る): to wring, squeeze, press, extract, strain out, contract ....
A camera's or eye's iris/aperture is also "shibori", because it contracts to constrict light.
But the most important shibori, vastly overshadowing quaint tie-dying art forms and camera apertures, is "ichiban shibori": the first press of the malt in beer-making.
If you're interested in giving this a try, this is a great introductory indigo dye kit. Just a need a bucket and something to dye (pillow-case, dish-towel, or an old t-shirt).
I was in Japan recently and was hoping to find something Shibori to bring home as a souvenir/gift, but had a pretty difficult time coming across anything. I wondered if this was just because I am gaijin, or if it has become less commonplace in general (or both)?