AVR Reset pin for a long time
No, this should not cause a problem. The one thing you need to worry about is the electrical state of the I/O pins during reset. Determine what state all of the I/O pins go to during reset (probably to input mode, perhaps with a weak pullup) and make sure that whatever is connected to them will not be damaged or cause damage to the AVR itself. Remember that all input pins should be held at a valid logic level and not allowed to float. This may mean that you need to add pullup or pulldown resistors in places where you might not otherwise need them.

EDIT: Additional information from the Atmel ATmega168 datasheet (I added emphasis for references to reset):


  If some pins are unused, it is recommended to ensure that these pins
  have a defined level. Even though most of the digital inputs are
  disabled in the deep sleep modes as described above, floating inputs
  should be avoided to reduce current consumption in all other modes
  where the digital inputs are enabled (Reset, Active mode and Idle
  mode).
  
  The simplest method to ensure a defined level of an unused pin, is to
  enable the internal pull-up. In this case, the pull-up will be
  disabled during reset. If low power consumption during reset is
  important, it is recommended to use an external pull-up or pull-down.
  Connecting unused pins directly to VCC or GND is not recommended,
  since this may cause excessive currents if the pin is accidentally
  configured as an output


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