If I use --mtime=1970-01-01 on a machine set to CET (UTC+1), tar will create a file where the mtime field contains non-ASCII bytes and no null character: see the ffff ... f1f0 bytes in the dump below. I've tested with 1.27.1 and 1.29.
I'd expect tar to emit an error.
I discovered this because Python's tarfile module fails to open such files with "invalid header", since it expects this field to contain an ASCII number, as described in the docs:
> date
Thu Nov 16 13:31:44 CET 2017
> echo > testfile
> tar cf test.tar --mtime 1970-01-01 testfile
> xxd test.tar | head
00000000: 7465 7374 6669 6c65 0000 0000 0000 0000 testfile........
00000010: 0000 0000 0000 0000 0000 0000 0000 0000 ................
00000020: 0000 0000 0000 0000 0000 0000 0000 0000 ................
00000030: 0000 0000 0000 0000 0000 0000 0000 0000 ................
00000040: 0000 0000 0000 0000 0000 0000 0000 0000 ................
00000050: 0000 0000 0000 0000 0000 0000 0000 0000 ................
00000060: 0000 0000 3030 3030 3634 3000 3133 3133 ....0000640.1313
00000070: 3535 3500 3030 3131 3631 3000 3030 3030 555.0011610.0000
00000080: 3030 3030 3030 3100 ffff ffff ffff ffff 0000001.........
00000090: ffff f1f0 3031 3636 3432 0020 3000 0000 ....016642. 0...
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