Rachel Barney (see her informative SEP article on the subject) thinks not :
Because of [a] shared agenda, and because Socrates' refutation of Callicles can be read as a sketchy, perhaps deliberately unsatisfying rehearsal for the Republic, it is tempting to assume that the two figures represent a single philosophical position. But in fact, Callicles and Thrasymachus are by no means interchangeable...For her, everything hinges on whether Thrasymachus holds that injustice is a virtue and justice a vice.
According to Barney, Thrasymachus is largely a debunker. He's a 'conventionalist', who claims that there is no justice and injustice, and that talk of such things merely masks power relationships. But he holds back from making claims about what is right or wrong 'by nature'.
In contrast, Callicles, although he too debunks common ideas of justice as mere conventions, additionally claims that naturally crafty and brave persons, who are stronger than others, ought to dominate over them. He asserts a morality of the naturally strong.
Barney admits that it might seem as though Thrasymachus takes that extra step also:
...it is worth asking what Thrasymachus‘s ideal of the ‘ruler in the strict sense’ adds to his account of justice. It seems to confirm that he is no conventionalist, since that view involves treating all actual laws as equal while on Thrasymachus' account not every regime counts as the real thing. More problematically, Thrasymachus' glorification of tyranny renders retroactively ambiguous his slogan, ‘Justice is the advantage of the stronger’. His praise of the expert tyrant (343b-c) suggests that, in addition to the debunking theses noted earlier, this slogan may also mean something like: it really is right and proper, part of the due order of things, for the strong to take advantage of the weak. This is precisely the claim that, as we will see, is expressed in the Gorgias by Callicles' theory of ‘natural justice’. If Thrasymachus too means to make this claim then he, like Callicles, evidently has what we may call a moral world-view — a view, that is, about how the world ought to be.But what clinches it for her is that Thrasymachus, she thinks, 'weasels out' of saying that justice is a vice and injustice a virtue:
However, as we have seen, Thrasymachus only flirts with the revision of ordinary moral language which this view would imply; when Socrates suggests that according to him justice is a vice and injustice a virtue, he weasels out.When precisely does he weasel out? According to Barney:
When Socrates asks whether, then, he holds that justice is a vice, Thrasymachus instead defines it as an intellectual failing: “No, just very high-minded simplicity,” while injustice is “good judgment” and is to be “included with virtue and wisdom” (348c-e).However:
(i) I don't see how, in this passage, Thrasymachus' 'including injustice with virtue and wisdom' (e)n a)reth=j kai\ sofi/aj tiqei=j me/rei th\n a)diki/an ) is not the same as his 'holding' that it is a virtue.
(ii) A few lines later Thrasymachus agrees that he regards injustice is 'something noble and powerful' and that he attributes to it 'all the other things that people attribute to justice' (fh/seij au)to\ kai\ kalo\n kai\ i)sxuro\n ei)=nai kai\ ta)=lla au)tw=| pa/nta prosqh/seij a(\ h(mei=j tw=| dikai/w| proseti/qemen, 348e9-10). It would be bizarre for him to say this but then deny that injustice is a virtue. And it would be even more bizarre for him to say this but deny that it was good to be unjust, that one 'should' be unjust if possible.
(iii) In the refutation that follows, Socrates, in arguing against Thrasymachus, explicitly takes him to be maintaining that an unjust person, as such, is good and wise (fro/nimo/j te kai\ a)gaqo\j o( a)/dikoj, 349d3).
(iv) After the refutation is over, Socrates implies that refuted view was that justice is a vice and a kind of foolishness, but injustice is a virtue and a kind of wisdom (diwmologhsa/meqa th\n dikaiosu/nhn a)reth\n ei)=nai kai\ sofi/an, th\n de\ a)diki/an kaki/an te kai\ a)maqi/an, 350d4).
In sum: Barney's view cannot be sustained. Her view that Thrasymachus is distinct from Callicles hinges on the claim that Thrasymachus 'weasels out' of saying that injustice is a virtue. But Thrasymachus does not weasel out of this; in fact, he says so rather plainly.