Would this image steganography technique be effective at avoiding detection?
On the one hand, I think that this could be considered a first step into the direction of adaptive steganography, because you do not use some blocks that you think that are easy to detect. In adaptive steganography we modify only the pixels of the image that are more difficult to model statistically and, consequently make the detection harder.
On the other hand, you use a $2\times 2$ block for hiding one bit so you are reducing the capacity. And for doing this, in some cases you need to make two changes! Two changes for hiding a bit is far from being optimal.
Currently steganography is much more advanced than this. You have cost functions that tell you which are appropriate zones of the image to hide information (the state of the art in spatial domain is the HILL [1] cost function), and matrix embedding techniques [4] that allows you to hide a lot of information modifying very few pixels. There is also a field that deals with Wet Paper Codes[2, 3], that makes possible reading a message without knowing which pixels have been modified. This gives you a lot of flexibility for building systems where you don't want to modify some kind of pixels.
[1]. A new cost function for spatial image steganography. Bin Li; Ming Wang; Jiwu Huang; Xiaolong Li. 2014 IEEE International Conference on Image Processing (ICIP), Paris, 2014, pp. 4206-4210.
https://projet.liris.cnrs.fr/imagine/pub/proceedings/ICIP-2014/Papers/1569891955.pdf
[2]. Writing on Wet Paper, J. Fridrich, M. Goljan, P. Lisonek, and D. Soukal, IEEE Trans. on Sig. Proc., Special Issue on Media Security, Eds. T. Kalker and P. Moulin, vol. 53, pp. 3923-3935, October 2005.
http://www.ws.binghamton.edu/fridrich/Research/WPC_TransactionsJournal1.pdf
[3]. Minimizing Embedding Impact in Steganography Using Trellis-Coded Quantization, J. Fridrich, T. Filler and J. Judas, Proc. SPIE, Electronic Imaging, Media Forensics and Security XII, San Jose, CA, January 17–21, pp. 05-01 - 05-14, 2010.
http://www.ws.binghamton.edu/fridrich/Research/tcq_v3.pdf
[4]. Steganography in Digital Media (Principles, Algorithms, and Applications). Cambridge University Press. 2009. ISBN: 9781139192903.