The answer is $\fbox{No}$. We know that for any person, the person is telling the truth if and only if the person two seats to his\her left is a truthteller. This is equivalent to saying that any pair of people who are one person apart are either both truthtellers or both liars. Without loss of generality, let the names of the people be $P_1$, $P_2$, $P_3$,... $P_{2017}$. Let $a_i$ be $1$ if $P_i$ is a truthteller, and $0$ if a liar. We have $a_i=a_{i+2}$ for all $i\in\{1,2,3,\ldots,2017\}$, where all indices are taken modulo $2017$. Hence, $$a_1=a_3=a_5=\cdots=a_{2015}=a_{2017}=a_2=a_4=\cdots=a_{2016}$$which means that the people are either all truthtellers, or all liars, which is a contradiction.

The answer is $\fbox{Yes.}$ Let the people be $P_1$, $P_2$, $P_3$, ..., $P_{5778}$. Consider when all odd numbered people are truthtellers, and all even numbered people are liars.