Glad you did not. 20K limit is almost a Insult, I understand few might say here that you're just starting off & are new to credit but still wait ... Kotak will offer a higher limit & a better card. Just try shift all your transactions to Kotak for a while at least (In case you do not want to take the offline C2C route).
NO. At this stage they would NOT have even done the hard enquiry, however you might start getting "the" sales calls, just do not give in to the temptation. Kotak offers good limits, just wait a bit bro ... Don't take 20K ... I started off my Kotak CC journey with 1.37L in 2014 with hardly any relationship with them till then.
When you do get the limit enhancement with HDFC, visit your Kotak home branch & try offline C2C, in all likelihood they will match your existing limit .. Since you are pre approved, Kotak will issue you a card regardless the route you apply. Also, try negotiating for a better card, league platinum is a dead card.