No. My interpretation of UNF-57 is that this would apply only to vessels and structural parts of vessels fabricated from non-ferrous materials. The structural parts of the vessels would be welded heads and nozzles or other appurtenances. If you read the paragraph it references inspections of vessel fabrication welds to be performed in accordance with UW-11.

UW-11 in Section VIII, Div 1 specifies UT or RT of vessel fabrication welds. The tubing in the heat exchanger would not be considered part of the fabrication welds of the vessel.

See UG-8 Is filler metal used?

deanc;
UG-8 ...refers to pipe or tubes that may be used as shells or as parts of the pressure vessel. In the case above, if the tubes are supplied in accordance with Section II, SB-338, as parts of the pressure vessel they already have been inspected and hydrotested per SB-338. So, there is no need to RT. This is my take on the situation.

metengr--no argument with you,just check UG-8(a). glothex does not state if this is a shell or heat exchanger tube.

UG-8 applies in both cases. ie: footnote 3,filler metal added? If so needs RT and a Partial Data Report for UNF. I have not looked at this spec.just a general statement.

Now if it is a shell,better see UW-12(e).

Of course additional requirements of UNF would need to be reviewed.

But in this case-does not one hand wash the other?

You sid it: "joints of categories A and B shall be fully radiographed in accordance with UW-51"
You should specify a little more.
As I understand, you used tube for a shell of the vessel,
if the longseam was welded by adding filler metal, you shall RT, if the tube was fussion welded w/o adding any filler, you may be okay if that specification(SB-338 Grade 2) is allowed as shell material for your vessel.
ER