It would seemingly only matter had there been a trial. Oswald didn't say much that could have used against him anyway other than a few lies like not owning a rifle. So it would not have made much difference even in a criminal trial to have excluded anything he said in the interrogation. There was a mountain of admissible evidence that convicted him a thousand times over. CTers attempt to blur the legal context from reality as though they are one and the same. They are not. Anyone interested in the case today doesn't have to concern themselves with whether Oswald's legal rights were protected in 1963. They can avail themselves of all the evidence to reach a conclusion as to his guilt.
Dave Reitzes had a quote (in the old forum) from Assisstant DA Bill Alexander where Alexander said that even AFTER reading Oswald his 5th Amendment right to remain silent (as required by Texas law at that time) that any statement he made *wouldn't* have been used against him. It was, he said, Dallas policy not to use them. The FBI also had a requirement to read suspect their rights to remain silent and to a counsel. Prior to Miranda most states required the police to read suspects those rights. Texas, however, did not REQUIRE that a lawyer be provided only that a suspect had the right to one; this is something that Miranda requires.
However Fritz testified that he read Oswald his right to remain silent several times because he knew that if he didn't any statements would be thrown out. Which is at odds with what Alexander said, i.e., that they didn't use them anyway. So why would Fritz be worried about the statements being tossed if the policy was not to use them?
So would Oswald's statements during the interrogation be used? Like a lot of things in this event you can argue it both ways.
As to denying counsel: As I noted above, Texas was not required to provide suspect a counsel only that they had a right to one. Which lawyer was denied Oswald? He wanted Abt and before it could be determined whether Abt would represent him (and Abt's behavior that Saturday was, to me, quite odd: it was like he was ducking the matter) it's clear to me that he, Oswald, didn't want another person.
The problem, in my view, with not getting Oswald a lawyer was due to Oswald's obstinacy and not because of anything the Texas authorities were doing.
I can't find the Alexander quote anywhere but I don't doubt that Dave had it correctly.