I am not sure why a print would not work; it would just be more difficult for matching, require more fabric for drop-match and more time consumption of button-covering. Houndstooth or any small print/check, etc., should be very easy to work with.

IMO a smaller & subtle houndstooth would work but larger one in contrasting colors would appear too busy & obscure the tufted details.

Tufting distorts the fabric pattern, since the button makes the fabric go in and out, specially a very regular and contrasting linear one, harlequin for example; how big is your houndstooth pattern?

It could end up looking like Op Art. A smaller pattern could work, but the check pretty much cancels the tufting detail.

Gosh, I had a tufted back sofa from Ethan Allen with a large jacobean print back in the 1960s and it was gorgeous and had no problems.