Answer

No. That will not allow you to avoid taking your RMD.
Under the RMD regulations, the December 31 fair market value (FMV) used to calculate your RMD must be calculated as follows:

December 31 FMV + http://retirementdictionary.com/definitions/outstandingrollover outstanding rollover contributions + http://retirementdictionary.com/definitions/outstandingtransfer outstanding transfers + http://retirementdictionary.com/definitions/outstandingrecharacterization outstanding recharacterizations of IRA or Roth contributions

• Outstanding rollovers are rollover contributions of distributions taken from a traditional IRA, http://retirementdictionary.com/definitions/substantiallyequalperiodicpaymentsepp SEP IRA or http://retirementdictionary.com/definitions/simpleira SIMPLE IRA that are timely rolled over to another traditional, SEP or SIMPLE IRA after December 31
• Outstanding transfers are transfers initiated before the end of the year and left the delivering traditional, SEP or SIMPLE IRA before December 31, but did not get credited to the receiving traditional, SEP or SIMPLE IRA until after December 31
• Outstanding recharacterizations are IRA or Roth contributions that are timely recharacterized after December 31

Therefore, in the example you gave, you are required to add (back) the amount that you rollover within 60-days to your December 31 FMV, in order to determine your correct RMD amount.

In short; you cannot avoid taking your RMD by completing a distribution before year-end, only to rollover the amount (within 60-days) after the end of the year.