In general- anything can be submitted for publication. Whether or not it gets accetped is a harder question, and one you are not going to get from a discussion forum.
A lot goes into deciding whether or not a paper gets accepted by a given journal, including quantifiaible factors (# patients, study design- RCT > Phase I or II > retrospective, etc). Other factors include relevance to readers, novelty of question or study, appropriateness of statistics, etc.
If you want a free gauge of the quality of a potential paper- submit an abstract to a national meeting. Alternatively, simply write the paper and submit it to your journal of choice. A rejection at one journal does not mean that another journal will not accept it. A rejection should also give you feedback of what you could do to improve it.
Lastly- the data is what it is, and p values should not impact if a paper is acceptable or not. One should strive for a well-designed study and not a give p value. For example: a p value 0.05 is not magically different than a p value of 0.06- one means a 6% risk that the null hypothesis (equivalence) is true, and the other 5%.
So my suggestion- write it up and submit it, and have a good explantion why you have a poor correlation and sign. p value.