If I build with --without-iconv, I get this result when running ./runtest:

$ ./runtest 
## XML regression tests
File ./test/ebcdic_566012.xml generated an error
## XML regression tests on memory
File ./test/ebcdic_566012.xml generated an error
## XML entity subst regression tests
File ./test/ebcdic_566012.xml generated an error
## XML Namespaces regression tests
## Error cases regression tests
## Error cases stream regression tests
## Reader regression tests
Result for ./test/ebcdic_566012.xml failed
File ./test/ebcdic_566012.xml generated an error
## Reader entities substitution regression tests
Result for ./test/ebcdic_566012.xml failed
File ./test/ebcdic_566012.xml generated an error
## Reader on memory regression tests
Result for ./test/ebcdic_566012.xml failed
File ./test/ebcdic_566012.xml generated an error
## Walker regression tests
Failed to parse ./test/ebcdic_566012.xml
File ./test/ebcdic_566012.xml generated an error
## SAX1 callbacks regression tests
Failed to parse ./test/ebcdic_566012.xml
File ./test/ebcdic_566012.xml generated an error
## SAX2 callbacks regression tests
Failed to parse ./test/ebcdic_566012.xml
File ./test/ebcdic_566012.xml generated an error
## XML push regression tests
Failed to parse ./test/ebcdic_566012.xml
File ./test/ebcdic_566012.xml generated an error
## HTML regression tests
## Push HTML regression tests
## HTML SAX regression tests
## Valid documents regression tests
## Validity checking regression tests
## General documents valid regression tests
## XInclude regression tests
## XInclude xmlReader regression tests
## XInclude regression tests stripping include nodes
## XInclude xmlReader regression tests stripping include nodes
## XPath expressions regression tests
## XPath document queries regression tests
## XPointer document queries regression tests
## xml:id regression tests
## URI parsing tests
## URI base composition tests
## Path URI conversion tests
## Schemas regression tests
## Relax-NG regression tests
## Relax-NG streaming regression tests
## Pattern regression tests
## C14N with comments regression tests
## C14N without comments regression tests
## C14N exclusive without comments regression tests
## C14N 1.1 without comments regression tests
## Catalog and Threads regression tests
Total 2828 tests, 10 errors, 0 leaks


Other tests (e.g. Python tests, "make tests") fail similarly.

The ebcdic_566012.xml file needs to be excluded from the test suite when building sans iconv. Given the heavy use of globs, I think the easiest route would be to move the file to a new subdirectory ./test/ebcdic/ (and similarly with the result files), and include ./test/ebcdic/* when WITH_ICONV/LIBXML_ICONV_ENABLED is set appropriately.