Behavior Differences Running SQL 2017 in 130 Compat Mode vs. Running SQL 2016 in 130 Compat Mode?
It will not behave exactly the same. Compatibility mode works at the database level, not the Instance level, which is still 2017. But it will mostly work the same.

I would check the breaking feature list for 2017 as some Instance level changes may still affect your code, despite it being in 2016 compatibility mode. However, the breaking changes from 2017 are relatively minor so it is probably unlikely you'd be affected. In general, some version breaking changes are covered under compatibility mode and some are not.

The documentation gives good examples of this,


  For example, the FASTFIRSTROW hint was discontinued in SQL Server 2012
  (11.x) and replaced with the OPTION (FAST n ) hint. Setting the
  database compatibility level to 110 will not restore the discontinued
  hint.


and


  An example of a breaking change protected by compatibility level is an
  implicit conversion from datetime to datetime2 data types. Under
  database compatibility level 130, these show improved accuracy by
  accounting for the fractional milliseconds, resulting in different
  converted values. To restore previous conversion behavior, set the
  database compatibility level to 120 or lower.


You should also look at the deprecated feature list for 2017 and try to remove any of those areas from future development in order to future-proof your applications. And of course, any new features from 2017 may require updates to take advantage of them as well, but I get the impression you're more concerned about breaking changes. 



With all that said, you're probably fine, but should still carefully and thoroughly test upgrading the compatibility mode before moving it to production.