'Yes, of course'  this would be my answer too. But can I suggest some nonKID options, in the Modern move order after 3 c4, in addition to the ones Alumbrado mentions?
I'm thinking of taking up the Modern next season, and against 3 c4 I'm intending to play one of these two systems (the second of which will often transpose to the first):
SYSTEM ONE: 3 ...d6 4 Nc3 c5!?:
I haven't closely looked at 5 Be3 Nf6!? or ... Qa5!?, but I assume this isn't critical; meanwhile 5 Nge2 cd (there are other moves!) transposes to 5 Nf3 cd. I also assume that 5 dc dc (5 ...Bc3 may be interesting?) 6 Qd8 Kd8 is OK for Black. That leaves 5 Nf3 and 5 d5 as the most critical tries. Against 5 Nf3, Black has either (1) 5 ...cd 6 Nd4 Nc6 or ...Nf6, both of which should end up as a Maroczy Bind Accelerated Dragon, or (2) 5 ...Nc6 6 d5 Nd4 7 Nd4 cd, transposing to the line 3 c4 d6 4 Nc3 Nc6 5 d5 Nd4 6 Nge2?! (6 Be3!) c5 7 Nd4 cd, which according to Nigel Davies is unclear after 8 Nb5 Qb6 9 c5 dc! 10 Bf4 Kf8. If neither of these two options appeals, Black can also try Topalev's 5 ...Qa5!?. Against 5 d5, since 5 ...Nf6 is not necessarily either a KID or even good, I'm intending 5 ...e6. Now White has three main tries (in addition to 6 de!?, after which all three responses have been seen!). After (1) 6 Nf3, NCO (p. 69, n. 33) gives 6 ...Ne7 7 Be2 00 8 00 a6 (8 ...e5!? may be interesting too) 9 a4 ed 10 cd without an assessment (and as transposing to a position it seems not to mention!), while also possible here is 7 Bd3 00 8 00 a6 or ...e5. Alternatively there's (2) 6 Bd3 ed! (6 ...Ne7?! 7 h4! ed 8 cd! is a bit better for White while 6 ...Nf6?! 7 Nf3 leads to KID lines [NCO p. 523] where White can obtain a bind if Black takes on d5 and White replies with exd5!, or a small edge if he doesn't) 7 ed!? (7 cd Nf6! is a Benoni) Ne7!? 8 Nf3 (8 Nge2!?) 00 9 00 Nd7!? (9 ...Bg4!? and 9 ...h6!? have also been seen) intending ...Ne5 with a reasonable position. Finally, on (3) 6 f4, 6 ...Nf6 7 Nf3 00 (or 7...ed first) is a Four Pawns Attack, but Black can also try 6 ...Ne7!?, or 6 ...ed!? 7 cd and now 7 ...Ne7 (7 ...Nf6?! 8 Bb5! being a Taimanov Benoni).
SYSTEM TWO: 3 ...c5!?:
I assume (rightly or wrongly!) that 4 Be3, 4 Ne2 and 4 dc aren't critical. This leaves 4 Nf3 and 4 d5. Against the first, Black has 4 ...d6, when 5 Nc3 transposes to 5 Nf3 in System One, while if this doesn't appeal he can try Rausis's 4 ...cd 5 Nd4 Qb6!? 6 Nb3 d6!, which according to NCO (p. 63, n. 50) is OK. After 4 d5, 4 ...d6!? (4 ...e6 seems sound too but I can't see any advantages to this move order) will probably transpose into System One lines whether White plays 5 Nc3, 5 Nf3, 5 Bd3 or 5 f4 if Black responds to each of them with 5 ...e6, but there are also a few independent possibilities that might be interesting: (1) 5 Bd3 e5!?; (2) 5 f4 e5!?; and (3) 5 f4 Nf6 6 Nc3 00 7 Nf3 e5!? (7 ...e6 8 Be2 ed 9 cd is a Benoni).
I've always considered that the existence of a number of different ways of playing it is a sign of the health of a system (if one line should be refuted the others are still alive!), and this seems to be the case here. But I'm not a strong player and all of this should be carefully checked. Anyway, the above is my tentative attempt at questioning Botvinnik's reported statement that nonKID 3 c4 lines are dubious for Black. Your opinions are eagerly sought!
