I am made to believe so, but it all depends with the network used by your Internet Service Provider. If they are using 3G, then Samsung Note 3 will pick up the 3G signal. Note 3 has a network support of GSM, GPRS, EDGE, HSPA(3G) and HSPA+ which i believe Samsung terms as 4G. There's a controversy though whether HSPA+ is really a 3G, because its considered that LTE is the real 4G. Most tech experts term HSPA+ as a faster 3G, while others consider it as 4G.
But the fact is, if Samsung note supports HSPA+, then its faster than the other handsets that only support HSPA. so, yeah, I'd say Samsung Note 3 is a 4G, because its faster than 3G.