Does an Earley parser equipped with LL(1)-style lookahead parse in linear time for all LL(1) grammars?

If a standard Earley parser (with proper handling of nullable non-terminals, see Section 4 of "Practical Earley Parsing" by Aycock and Horspool) is modified with LL(1)-style lookahead, does it then parse all LL(1) grammars in linear time?

To be precise with "LL(1)-style lookahead", I reproduce the $$\text{Predictor}$$ and $$\text{Completer}$$ steps of the Earley algorithm, with modifications in bold:

$$\text{Predictor}$$. If $$[A \to \ldots\bullet B\dots, j]$$ is in $$S_i$$, add $$[B \to \bullet \alpha, i]$$ to $$S_i$$ for all rules $$B \to \alpha$$ where $$x_{i+1} \in \text{FIRST}(\alpha)$$ or $$\alpha \Rightarrow^* \lambda$$.

$$\text{Completer}$$. If $$[A \to \ldots \bullet, j]$$ is in $$S_i$$, add $$[B \to \alpha A \bullet \beta, k]$$ to $$S_i$$ for all items $$[B\to \alpha \bullet A \beta, k]$$ in $$S_j$$ where $$x_{i+1} \in \text{FIRST}(\beta)$$ or $$\beta \Rightarrow^* \lambda$$.

This is also assuming (for the purposes of this lookahead) that the input is augmented with an EOF symbol $$\$$. Note that all $$\text{FIRST}$$ invocations occur on suffixes of productions, and can be precomputed and stored in a table indexed by production number and dot location.

I am aware of the work by Joop Leo that augments an Earley parser to parse all LR(k) grammars in linear time, but I am curious if just the above is enough for LL(1).

As an example grammar where the above reduces complexity, the grammar $$S\to a S \mid \lambda$$ normally has an quadratic number of Earley items which goes to linear with the above optimization.