Proper error return code?

The error numbers used by net helpmsg and ErrorLevel are totally different things; net helpmsg only understands error numbers returned by the net command.

What you are trying to accomplish is the following, I think (take a look at the explanatory remarks):

rem /* Test whether `java` is installed and can be found: */

rem // simply try to run the `java` executable:
java -version 2> nul
if ErrorLevel 1 echo ErrorLevel is set to %ErrorLevel% [9009 if not found, 0 otherwise].

rem // or use the `where` command to find the `java` executable:
where java > nul 2> nul
if ErrorLevel 1 echo ErrorLevel is set to %ErrorLevel% [1 if not found, 0 otherwise].

if ErrorLevel 1 goto :EOF

rem /* Thest whether the Java script `name.jar` exists: */

rem // simply try to run the Java script:
java name.jar -commands 2> nul
if ErrorLevel 1 echo ErrorLevel is set to %ErrorLevel% [1 if not found, or, if the script exists, its `ErrorLevel`].

rem // or use the `where` command to find the `java` executable:
where name.jar > nul 2> nul
if ErrorLevel 1 echo ErrorLevel is set to %ErrorLevel% [1 if not found, 0 otherwise].

rem /* (the `> nul` suffix suppresses output messages,
rem     the `2> nul` suffix suppresses error messages) */


rem /* To capture the error message returned by any command, do this: */
for /F delims^=^ eol^= %%E in ('
    command 2^>^&1 ^> nul
') do (
    echo This is the error message: "%%E"
)

Since the question post has been updated and clarified, the following does not cover the problem. The true solution can be found above. I keep the former answer here for reference.
This is for the case you want to extract the error number returned by the net command, which is specific to this command and has got nothing to to with the ErrorLevel:

The error number of the net command and the ErrorLevel are totally different things.

Supposing you try to execute net view, it might fail with this error message, for instance:

System error 6118 has occurred.

The list of servers for this workgroup is not currently available

The resulting ErrorLevel is 2 though.
So executing net helpmsg %ErrorLevel% does not make any sense.

In contrast, net helpmsg 6118 does, which returns the following string:

The list of servers for this workgroup is not currently available

To capture the error number of the net command, use a for /F loop and take the line of the first iteration only by an if defined condition (using command net view in this example):

set "ERRNUM=" & set "ERRTXT="
for /F "delims=" %%M in ('2^>^&1 ^> nul net view') do (
    rem Note that the `token` option is language-dependent:
    for /F "tokens=3" %%N in ("%%M") do (
        if not defined ERRNUM set "ERRNUM=%%N"
    )
    set "ERRTXT=%%M"
)

This would capture the error number 6118 of the above example and store it in variable ERRNUM. The last line of the error output (that I consider as the error message) is stored in variable ERRTXT.

To retrieve the error message later from a given error number stored in ERRNUM, you could use this:

set /A "ERRNUM+=0"
if %ERRNUM% NEQ 0 (
    for /F "delims=" %%M in ('net helpmsg %ERRNUM%') do (
        set "ERRTXT=%%M"
    )
)

Side Note: Yes, I would remove the quotes if %ErrorLevel% NEQ 0 to do a numeric comparison.