Quest for biological explanation of psychological processes and advancement in technology has attracted many researchers to neuroscience. psychologists are these days more inclined towards neuroimaging,single cell studies etc.
I agree with Sachchidanand that the general trend is there -- from a "softer" behavioral science towards more "hard" and biologically inspired science. However, due to the enormous complexity of the systems with self-regulation, communication and consciousness-related intentionality spanning from atomar to genetic to cellular to neural networks to systems to populations to cultures etc, traditional neuroscience/biology may remain limited in understanding all crucial processes and structures commanding these processes. So I believe that an interdisciplinary stance should be developed and hopefully will succeed. (Biophysics, biochemistry, neurobiology, psychology, sociology, cultural and semiotic studies, philosophy -- all these and more are continually needed. But their mutual understanding and possibility to meaningfully translate their concepts should improve considerably.)
Is the psyche, in principle, reducible to nueroscience/biology? If it is then your answer is yes. However, if this were the case how would we explain social issues that are apart from our mere biology? Would we then start to blame our neurons instead of ourselves for crimes? Hmm...
... we blame ourselves, but doing so we also blame our neurons, but this latter aspect remains not mentioned, irrelevant in certain contexts, or not thought about.
It is important to realize that neuroscientific and behavioural methods analyze the same problems on a different level of analysis. Neuroscience can't really replace our mental mechanism accounts entirely. How much popularity neuroscience maintains will probably also depend on technological advancement. Let's face it: a lot of the neuroscience work out there is glorified correlational work, with either really, really bad temporal resolution (e.g., fMRI) or really, really bad spatial resolution (e.g., EEG). There are newer techniques that look kind of promising, but I also think that neuroscience is frequently oversold. I'm neutral myself, but many people have a growing distaste for it.
As I see it, there are two issues as play here: questions and methods. For example, my degree is in cognitive psychology, but I am frequently identified as a cognitive neuroscientist as if it is something different. I find this a funny distinction because it seems to delineate methodology more than question. My questions are psychological in nature, and they can only be answered by taking a combined approach. I have to characterize the behaviors and phenomena that I want to understand. I can't do that using something like fMRI unless I first understand how to elicit/manipulate/engage the behaviors or cognitive functions of interest. At the very least, I must have an experimental design that captures the psychological phenomena of interest appropriately.
Although it is true that advances in biologically based methods have offered rich insights into cognitive functions, they can only do so because there is a strong history of behavioral work to serve as a backbone. (This can work in the other direction, too. Mechanisms elaborated in systems neuroscience have been known to inspire psychological questions.)
The upshot is that research in many facets of psychology is now inherently interdisciplinary--something that the APS and SFN have begun to embrace more heartily. Having biological explanations may enhance our understanding, but many fundamental questions are of a psychological and cognitive functional nature and will require integrating the biological basis with a psychological approach.
Of course it will! Basically, the human mind is just neurons firing. And neurons are biological systems. Unfortunately, the new fame of Biology won't last long because what's going on in the axons is electroCHEMICAL processes. So, chemistry will win the pot. But not ultimately, guess ...