Do regular monthly distributions from Simple IRA (not a Roth IRA) count towards withdrawing an excess contribution made to that IRA during the same year (2017)?

No.  Regular distributions do not correct an excess IRA contribution made in the same year.  Before the due date of the tax return for the year that the excess contribution was made, an excess contribution must be corrected by a special type of distribution (coded differently on Form 1099-R) called a "return of contribution."  The amount distribute as a return of contribution of a particular amount is required to be adjusted for any gain or loss while the amount being returned was in the IRA.

Thank you, dmertz.  Your answer was helpful.

If you are required to take RMDs then you must first satisfy the RMD amount before any other distributions can be considered return of excess.