Does Spearman's $r = 0.38$ indicate agreement? Can a Spearman correlation coefficient of 0.38 for a specific parameter  be considered to demonstrate reasonable agreement between two biological cell types, more specifically a cell line and a primary cell type? 
The parameter in question is the difference between percent of mRNA with and without last exon in two subcellular compartments, so for every gene (of which there are ~40000):
$\text{param} = x_{i} - x_{j}$,
where
$x_{i}$ is the proportion of RNA with  last exon in compartment $i$
$x_{j}$ is the proportion of RNA with last exon in compartment $j$.
For each cell type, this results in a table of
$\text{gene} - \text{param}$ 
And the Spearman correlation is found between the ranked order of this parameter in the two cell types.
Sample size is number of isoforms considered, in the order of 40000. Number of biological replicates per cell line - three each (standard in the field). 
 A: Correlations, such as Pearson's product moment correlation or Spearman's rank correlation, are not measures of agreement, no matter what their values are (i.e., even if $r = 1.0$).  
Consider a simple case using Pearson's correlation:  


  A guy takes a woman on a date to what he thinks is a nice restaurant.  Afterwards, they talk about the restaurant and give it a rating on a scale of $0 - 10$ for the overall experience (ambiance, service, food).  The guy rates it a $7$, his date a $1$.  So the next day, he takes her to a nicer place.  He rates it an $8$; she rates it a $2$.  The next day he takes her to an even nicer place.  He rates it a $9$; she rates it a $3$.  

Here are the ratings:  
guy woman
7   1
8   2
9   3

The correlation is $r = 1.0$.  You can decide for yourself if you think they agree on the quality of the restaurants.  I suspect this relationship isn't going to last.  
In essence, Pearson's correlation measures agreement with respect to the ordering of the ratings and the relative spacing between those ratings.  Spearman's correlation measures the agreement on the ordering only.  But people typically think of similar ratings as being at least as important as the ordering for there to be true agreement.  For continuous ratings, Lin's concordance coefficient can be used as a measure of agreement that isn't subject to these flaws.  For categorical ratings Cohen's kappa or Bangdawala's $B$ can be used to assess agreement instead of the chi-squared test for similar reasons.  
A: This is a question for your field. 
Here I comment generally on interpreting correlations. Specifically with your data, Spearman correlation might or might not be sensitive or insensitive to underlying patterns in scientifically helpful or unhelpful ways as compared with other possible correlations.  
If an advisor, supervisor,  mentor, experienced colleague or reviewer in your field considers "reasonable" to be, hmm,  reasonable wording in a report that explains the scientific context, your data, methods and results, then well and good for you. There is nothing in the statistics to allow direct quantifications of surprise, success or otherwise by just looking at correlations. 
In some fields correlations of 0.9 signal incompetent experimental technique and unpublishable results; in other fields correlations of 0.1 may flag the possibility of a real effect of interest or even of importance. For example, in many medical problems, all kinds of social or personal characteristics may have genuine but small effects on morbidity, mortality, life expectancy or other responses. 
All sorts of situations are conceivable. In a paper I reviewed, and recommended for rejection, authors proposed a new measure but results in their own paper could be used to show a very high correlation with existing measures, so it was nothing but a standard idea in a slightly different guise. Here by implication authors were suggesting something new but correlation showed that it was anything but. Discretion obliges that I cast a misty net over all the details, but this was a case where strong correlation was scientific failure and a weak correlation could have been more interesting. 
The vagueness of "a specific parameter" inhibits further comment; "two cell types" may allow some kinds of biologists to say more. 
