Yes, it will, since that's not how the difficulty adjustment works.
If you experience a drop of 90% in hashrate but only on the last 5-10 blocks the difficulty for the next week will still be nearly on the same value as the average for of the last 2016 blocks will be nearly the same, so you will still have the next two weeks period to deal with it till it adjusts 90% down. Same if the difficulty will drop in the middle of the period, you will only have 7 days of blocks being 10 times slower but also another two weeks of them being 5 times slower since the next period difficulty will be half of the original but still 5 times higher than how it should have been considering the last 7 days.
The hash rate doesn't affect the number of transactions being made and that is the only thing driving up fees.