Upgrading hardware for MySQL. If we get SSDs, are CPUs likely to become a bottleneck
I'm a proud owner of a Samsung 850 Pro for my desktop machine. It is a great disk, but it is not server-grade, and it is far from the PCI Flashcards sold by Virident and FusionIO (to put examples of some known brands). On the specialized hardware, a recent version of MySQL is almost a must, and some configuration tuning is needed to get most of them (change buffer, innodb checksums, transaction logs, doublewrite area, etc.). 

Check some of the vendor benchmarks (Oracle MySQL, MariaDB, Percona), as they usually boast its capabilities on those kind of devices.

However, a generalization cannot be reached- most of the problems are load-dependent. To give you an extreme example: if your queries all look like this:

SELECT AES_DECRYPT(*, key) FROM my_table;


Your CPU is probably going to be your bottleneck, while if you only insert new rows, then most of the delay will probably due to the disk latency. You should check if with the current hardware, the CPU load is high, that will probably increase with the new storage- but you may still hit other problems, like concurrency issues due to several threads trying to update the same row at the same time.


  assuming the current bottleneck is I/O and we replace the disks with SSDs, is it possible/likely for the E5-2620V2 CPUs to become the bottleneck


It is possible, but just with a bad configuration (what I mentioned before), assuming recent versions of MySQL (5.6, 5.7). Remember that SSDs are still way slower than the 1st cache level. You should probably ask again when the hardware is installed and meanwhile read sources like: 


http://www.percona.com/resources/technical-presentations/ssdflash-modern-open-source-databases-percona-mysql-webinar (generalities on ssds for databases)
http://dimitrik.free.fr/blog/archives/2013/10/mysql-performance-the-road-to-500k-qps-with-mysql-57.html (check the configuration used)
http://www.percona.com/blog/2013/10/03/inexpensive-ssds-database-workloads/ (optimizing MySQL for SSDs)
http://www.percona.com/live/mysql-conference-2013/sessions/you-know-ssd%E2%80%99s-make-mysql-fast-do-you-know-why
http://www.percona.com/live/mysql-conference-2012/sessions/transitioning-ssds-high-io-environment.