you are right, you don't neeed xOAth to make a search according to twitter search API.
If you want to use MGTwitterEngine you can use one of those methods :
// Search method
- (NSString *)getSearchResultsForQuery:(NSString *)query;
- (NSString *)getSearchResultsForQuery:(NSString *)query sinceID:(MGTwitterEngineID)sinceID startingAtPage:(int)pageNum count:(int)count; // search
- (NSString *)getSearchResultsForQuery:(NSString *)query sinceID:(MGTwitterEngineID)sinceID startingAtPage:(int)pageNum count:(int)count geocode:(NSString *)geocode;
You can find more details in MGTwitterEngine.h. It seems that you don't have to set authentification parameters to make a search, you just have to create an engine :
twitterEngine = [[MGTwitterEngine alloc] initWithDelegate:self];