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Has a relationship been noted?

Mostly, I'd like to know if the open interest increases on an underlying, does the underlying usually see increased trading?

My guess would be "yes" since MMs can only mostly hedge with the underlying, and they must constantly rehedge (buy or sell) the underlying everytime the underlying changes, possibly as volatility futures, interest rates, etc do too.

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"does the underlying usually see increased trading?"

Not necessarily. Most market makers do not re-hedge much in the underlying. In many markets the delta is exchanged (off-exchange) alongside the options trade at initiation, making both parties delta neutral at the outset. Re-hedges in large vol books are generally accomplished through other options and only residual delta is hedged in the underlying. But it obviously depends on the specific asset class and market convention as well as individual approach to trading such options. I am just saying that an academic paper will not be able to cover all those ifs, again it depends on above-mentioned variables.

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up vote 0 down vote accepted

Old (1998): http://bbs.cenet.org.cn/uploadimages/2003931633961531.pdf

Says that depth, volume, trade size, and trade frequency increase while spread decreases.

Since open interest is 0 before options trade and > 0 after, I'm going to extrapolate and say that increases in open interest increases underlying volume.

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