In order to be sure that your device is really connected to internet, at least you have to try a ping to a up&running at anytime server (like stackoverflow.com o google.com).
Of course, as suggested by @jonrsharpe in question's comments, if this check is necessary in order to understand if app can reach the web server, then a ping or something like that to your web server is also necessary.
But a ping to a surely working web server (like google) will give you the answer it your device is connected to internet (so your modem can reach internet), that way if your web server is not responding you can accordingly show a warning alert in your app to inform user that currently your server is unreachable.
Going to code, you can try to check connection status with Reachability
library like below
Reachability *reachability = [Reachability reachabilityWithHostName:@"stackoverflow.com"];
NetworkStatus networkStatus = [reachability currentReachabilityStatus];
and then check networkStatus
variable: if 0
you don't have access to internet, otherwise YES
, so
if(networkStatus==0) {
// no access to internet
} else {
// you have access to internet
}