Not really. Rapid growth in hashrate would only be slightly useful short term until the difficulty retargets which happens rather fast. This is only because you'd reduce the time between the blocks slightly so you may be able to squeeze a little more over some time period.

It really relies on blocksize median increasing, which is happening slowly - right now at 70kB. However, there's a problem with the current set-up (due to size of a single typical TX relative to min. blocksize) which ought to be fixed in the next HF. See here for more details: How can block size grow over time when miners are incentivised to keep size small?