Not quite. To "be away from the body" is clearly necessary for being "at home with the Lord", yet the text doesn't say that it's the only thing necessary: I Cor. 3:10-15 would seem to indicate the opposite.
IF IT WERE NOT SO (if there was interim millenia of flaming punishment) I WOULD HAVE TOLD YOU.
"If it were not so" refers to the existence of the "many mansions". And I will come again and receive you to Myself, that where I am, there you may be also does not indicate that there is no intervening state: the purpose of the reception is to that they may be in Heaven, yet they are not immediately placed in heaven after being received, so there seems no objection to supposing that they would go to heaven after making satisfaction for their sins.
Secondly, Jesus says, "no one comes to the Father but through Me". Catholic theology says "No one (except the very best) comes to the Father but through fiery purgatory."
The removal of sins in Purgatory is in virtue of the grace of Christ.
***yet the text doesn't say that it's the only thing necessary: I Cor. 3:10-15 would seem to indicate the opposite.***
I Cor. 3:10-15 has nothing to say to the issue you are addressing. It is a description of Judgement day.
***does not indicate that there is no intervening state:***
No "intervening state" is mentioned - in the entire NT. Nowhere does the NT state that there weren't cats and dogs numbered among Jesus' disciples. Are we free to infer that there were?
*** yet they are not immediately placed in heaven after being received,***
Where do you get this from?
***The removal of sins in Purgatory is in virtue of the grace of Christ.****
Where is Purgatory named in the NT?
Heaven is named 237 times. Hell/Death/Destruction is named nearly as many.