If my patent application is rejected in country of original filing (e.g. this country doesn't recognize software patents or even computer-implemented patents) will I be able to claim priority to it in foreign filings under Paris convention?
The Paris Convention has to do with the date of application not how the office deals with it. There is a 12 month limit to claiming a priority under Paris so by the time an application is rejected in the country of first filing it is probably too late for a second filing under Paris. If novelty hasn't been broken, you could still file in other places even without the priority benefit.