Yes, the vol swaps is precisely inside the Peter Carr framework : you suppose u are in a Black Scholes framework with a deterministic time-dependent volatility, u can write the today's expectation of the realized variance of the stock as a function of the todday's expectation of the logarithm of the stock at the expiry date.

Now by Carr's theorem, u can derive the expectation of the logarithm of the stock as a continuous portfolio of calls with different strikes (this portfolio can be discretized through a few (less than 10) options but this portfolio still contains far out of the money options)