What would make a practical difference would be to find an acceptable alternative location for the housing - petitions don't make any difference to planning decisions. SCDC has no option but to meet the objectively assessed housing need (you just need to keep an eye on the developing case law at examinations), and no amount of signatures can make the slightest legal difference: should they fail to do so developers could put in applications to build in all sorts of places which would provoke even greater opposition.
Petitions are essentially not useful in such cases, they're simply not something that's part of the legal process.