Can Earley parser work in parallel?
Yes, Earley's algorithm can be parallelized, but not in the way that you are thinking.
Earley's Algorithm In Particular
You ask about Earley's algorithm specifically. Parallelizing the algorithm in the way you suggest is unlikely to be faster. Researchers Peter Ahrens, John Feser, and Robin Hui report:

We first tried to naively parallelize the Earley algorithm by processing the Earley items in each Earley set in parallel. We found that this approach does not produce any speedup, because the dependencies between Earley items force much of the work to be performed sequentially.

The reason Earley's algorithm in particular is difficult to parallelize is because of interdependencies within the computation. To answer how successfully Earley's algorithm parallelizes, we need to solve this  demarcation problem: What should be call Earley's algorithm? Seth Fowler and Joshua Paul explain:

There  are  several  published  algorithms  (see,  for  example, Hill and Wayne[6]) for parallelizing a variant of the  the  Earley  algorithm,  the  CYK  algorithm.   Unfortunately,  in  practice  CYK  has  a  much  longer  running time than Earley (even though it has the same worst-case complexity of $O(n^3)$), and so it is not typically used.

Most researcher's agree that there are few successful parallelizations of the algorithm, however. Fowler and Paul continue:

For  the  Earley  algorithm  itself,  there  are  very  few parallelization  methods  published  (though  there  are many  optimizations—see,  for  example,  Aycock  and Horspool [1]).   One  such  method  by  Chiang  and  Fu [3] uses  a  decomposition  similar  to  the  one  we  develop,but goes on develop the algorithm for use on a specialized VLSI. Similarly, Sandstrom[7] develops an algorithm based on a similar decomposition....

Nonetheless, there are parallel versions. Peter Ahrens, John Feser, and Robin Hui who we cited earlier present &quot;the LATE algorithm, which uses additional data structures to maintain information about the state of the parse so that work items may be processed in any order. This property allows the LATE algorithm to be sped up using task parallelism.&quot; The researchers claim a &quot;120x speedup over the Earley algorithm on a natural language task.&quot;
Parallel parsing in general - usually impractical
Parallel parsing techniques have been studied for decades.  Other parsing algorithms are more amenable to parallelization, such as the CYK algorithm mentioned above. But parallelizing parsing is only rarely a practical strategy. Most parsing tasks you are likely to encounter are much more efficiently performed serially, that is, in the old fashioned single-threaded way.
The reason parallel parsing algorithms are generally impractical is because parallelism has a lot of overhead that needs to be recouped by the gain in speed, while most parsing tasks can be performed incredibly quickly. (See parallel slowdown.) Quoting from Parsing Techniques: A Practical Guide, by Dick Grune and Ceriel J. H. Jacobs:

From a practical point of view, parallel parsing is interesting only for problems big enough to require considerably more time than a fraction of a second on a single processor. There are three ways in which a parsing problem can be this big: the input is very long (millions of tokens); the grammar is very large (millions of rules); or there are millions of inputs to be parsed. The last problem can be solved trivially by distributing the inputs over multiple processors, where each processor processes a different input and runs an ordinary, sequential, parser. Examples of very long inputs requiring parsing are hard to find. All very long parsable sequences occurring in practice are likely to be regular: generating very long CF sequences would require a place to store the nesting information during sentence generation. ...
The situation is different for parsing with very large grammars. These are found most often in linguistics. They are especially bothersome there since most linguistic applications require general CF parsing techniques, the speed of which depends on the grammar size.

References
Seth Fowler and Joshua Paul. &quot;Parallel Parsing: The Earley and Packrat Algorithms.&quot; (2009). Note that this is a student project report for an undergraduate course.
Peter Ahrens and John Feser and Robin Hui. &quot;LATE Ain’T Earley: A Faster Parallel Earley Parser.&quot; (2018) The arXiv, 1807.05642.
Grune D., Jacobs C.J.H. (2008) Parallel Parsing. Parsing Techniques. Monographs in Computer Science. Springer, New York, NY.