Can Status of NOEXEC be Checked with a DMV?
NOCOUNT can be determined for the current session by parsing @@OPTIONS or by running DBCC USEROPTIONS.
Unfortunately, the only way I could find to determine the value of this option for a different session is by capturing the ExistingConnection event in SQLTrace or Extended Events.

Example 1:

DBCC USEROPTIONS


Output:

+-------------------------+----------------+
|       Set Option        |     Value      |
+-------------------------+----------------+
| textsize                | 2147483647     |
| language                | us_english     |
| dateformat              | mdy            |
| datefirst               | 7              |
| lock_timeout            | -1             |
| quoted_identifier       | SET            |
| arithabort              | SET            |
| ansi_null_dflt_on       | SET            |
| ansi_warnings           | SET            |
| ansi_padding            | SET            |
| ansi_nulls              | SET            |
| concat_null_yields_null | SET            |
| isolation level         | read committed |
+-------------------------+----------------+


Example 2:

SELECT *
FROM (
    VALUES  
    (1     ,'DISABLE_DEF_CNST_CHK'),
    (2     ,'IMPLICIT_TRANSACTIONS'),
    (4     ,'CURSOR_CLOSE_ON_COMMIT'),
    (8     ,'ANSI_WARNINGS'),
    (16    ,'ANSI_PADDING'),
    (32    ,'ANSI_NULLS'),
    (64    ,'ARITHABORT'),
    (128   ,'ARITHIGNORE'),
    (256   ,'QUOTED_IDENTIFIER'),
    (512   ,'NOCOUNT'),
    (1024  ,'ANSI_NULL_DFLT_ON'),
    (2048  ,'ANSI_NULL_DFLT_OFF'),
    (4096  ,'CONCAT_NULL_YIELDS_NULL'),
    (8192  ,'NUMERIC_ROUNDABORT'),
    (16384 ,'XACT_ABORT')
) AS v(num, descr)
WHERE @@OPTIONS &amp; num = num;


Output:

+------+-------------------------+
| num  |          descr          |
+------+-------------------------+
|    8 | ANSI_WARNINGS           |
|   16 | ANSI_PADDING            |
|   32 | ANSI_NULLS              |
|   64 | ARITHABORT              |
|  256 | QUOTED_IDENTIFIER       |
|  512 | NOCOUNT                 |
| 1024 | ANSI_NULL_DFLT_ON       |
| 4096 | CONCAT_NULL_YIELDS_NULL |
+------+-------------------------+


Unfortunately, I could not find a way to tell whether NOEXEC is on or off.