IOPS needs of Root Volume vs Database/Log Files Volume
A 'gp2' EBS volume will have plenty of performance for use as a root volume. There won't be any problems.

See details on EBS gp2 volumes on Amazon's documentation.


  General Purpose (SSD) volumes [... have ...] the ability to burst to 3,000 IOPS for extended periods of time, and a baseline performance of 3 IOPS/GiB up to a maximum of 10,000 IOPS (at 3,334 GiB).


...


  Volumes earn I/O credits every second at a baseline performance rate of 3 IOPS per GiB of volume size. For example, a 100 GiB General Purpose (SSD) volume has a baseline performance of 300 IOPS.


You'll be fine. Your root volume shoudn't be doing tons of I/O anyway. Frequently used data like program binaries will be cached in the kernel buffer caches in instance RAM. You're mainly looking at write activity for log files, etc, and it's unlikely that'll be a problem.

Do make sure, if you log via syslog, that flushes are not forced after each log write though. That usually involves prefixing the log output line with a -.