In Joyce's "Eveline," no, Eveline is not going to Argentina to be a prostitute. Why would you think that? Is that what you think of when you think of Argentina? There is nothing whatsoever in the story about Eveline going into prostitution. She is a 19-year-old woman with a lousy life who meets a sailor and wants to go away.
The importance of the photo is that the priest pictured is one more person to add to the list of people who have left Ireland. The story is filled with people who leave Ireland, and that is what Eveline wants to do.
The photo is described as yellow because it's deteriorated; it's old. And of course this, by extension, suggests the state of Ireland itself.
That's a bit of a tenuous connection, but I can see why you might consider that - the boyfriend in the short story "Eveline" by James Joyce might well not have Eveline's best intersts at heart and may be out to exploit her naivety. However, I think we should concentrate on the actual facts that James Joyce gives us in the story text. We know that Eveline has a strong sense of duty towards her dead mother's wish to have her family looked after when she has passed on. We know she goes dutifully to her shop job day in, day out. We know she does her best by her siblings despite the strain of mistreatment by her neglectful father. Is she the type to fall into this type of exploitation? The color yellow enhances the mood of faded gentility in the story - it is the colour of age.
Actually, it's extremely likely that Eveline would have faced prostitution in Buenos Aires. Research the history of Irish immigration to Argentina...Many Irish people emigrated at that time with the promise of a better life only to arrive and be worse off. Look up the City of Dresden situation in 1889. It's really interesting....