Yes. The most common application for group 3 compression (more precisely CCITT T.4) is for FAX image. In this case, the image is by definition a two-level (1 bit) image, and a single compression is expected. Therefore, if you are not doing anything except that the compression value (tag 259) is “2” (for a two-level image), then this is understood as encoding G3 1 (modified by Huffman). The only other parameters are compression (1) and packet bits (32773). All three types of coding should be supported by basic readers, but my experience has shown that many readers do not support group III compression support, especially G32D.
G31D is much easier to implement than G32D, but not so effective. The G31D saves each scan line individually, while the G32D saves the differences between scan lines. This can significantly affect the amount of data needed to determine the image, such as a typical facsimile image, where most of the image is blank white paper.
If you want to use G3 2-dimensional coding, you should be more specific in tags. You must use CCITT encodings to specify the T4 compression encoding (CCITT T.4 is the "real" name for the Group 3 encoding standard). To indicate this, set tag 259 == 3. Then set T4 to 2-dimensional coding. The T4 parameter tag (tag 292) is a bit more complicated compared to simple tags such as the standard compression tag (259). This is a LONG type used as a set of 32-bit flags. If you leave all bits equal to zero, then by default one-dimensional encoding is used (does not differ from this tag).
For 2-dimensional coding, you must set the zero bit (least significant bit) to 1. (If you use more than one strip, each strip should obviously start with a 1-dimensional scan line.) Bit 1 is set to 1 only if used uncompressed mode. Bit 2 is used to indicate whether padding bits were used to keep the EOL at the byte boundary (set to 1 if true). All other bits are zero by default.
Remember that most readers do not understand all the options available in TIFF. This is an extremely powerful format, but it makes it difficult to implement outside the TIFF baseline (which probably processes 90% + TIFF images). If you use 3-D encoding of group 3, you can expect that most readers who specifically support fax images and medical images * will decode the image correctly. I would not have hoped much more.
(TIFF is not a standard medical image format, but I believe that readers supporting DICOM and TIFF images usually support the full TIFF standard)
This answer is longer than I expected. If I have not answered your question yet, check in my original post, and I will edit my answer.
EDIT: You can find the TIFF standard and other supporting documents on the Adobe developer site. http://partners.adobe.com/public/developer/tiff/index.html