No
She's able to access the Avatar State because of Raava. The Avatar State literally is Raava's power. However, since Raava "died" once, all the previous reincarnations were lost. When Raava came back to life, and merged with Korra, Korra restarted the cycle, thereby having no previous connections to access.
So, if we were to sort things by Raava's lives, it would be that:
Korra is the Last Avatar of Raava's 1st Life & the First Avatar of Raava's 2nd Life
I have a theory that if Korra accessed the Avatar State while in the Tree of Time, Raava may be able to remember the past lives, but that won't necessary allow Korra to directly access them