Can I invest SBI blue chip fund direct growth for 10 to 12 years through SIP?

Sure, go ahead and invest in a good equity mutual fund. 10–12 years is a good horizon to go for equities. As your corpus builds do diversify to minimise risk.

If you invest just ₹ 1000 in a fund giving you 15% in the long run, you will end up with ₹ 4.03 lakhs. Invest ₹ 10k and the corpus becomes ₹ 40.3 lakhs.

Avoid regular plan funds with brokers (look for the words Direct Plan).