In principle, this should not be a problem - the method is openly available, and the reviewers should be able to make up their mind on it based on public information.
In practice, whenever you submit a paper where a core element is a method in a separate paper, reviewers cannot evaluate in too much depth the prior work it is based on - this would ask them to referee two papers at once! Referees will use rough heuristics to determine how much criticism to apply to that method, and in some cases could decide that it is not worth refereeing your second paper until your first is published. If you have too many negative signs and not enough positive ones, you might have trouble:
Positive signs:
- algorithm applied in other papers successfully
- algorithm has rigorous mathematical proof backing it
- initial paper comes from group with strong reputation
- initial paper published in well-respected journal/conference
- algorithm seems "reasonable," i.e. not shockingly more effective than state of the art
Negative signs:
- paper makes outlandish claims of effectiveness, but hasn't been applied or discussed by any other papers
- paper has been on arxiv for years, but isn't published yet
Not all of these are good scientific principles! And if your method is interesting, and appears sensible, referees will put more time into understanding it than this rubric indicates. But I think that this predicts how referees can think about this sort of question.
