The answer is undoubtedly yes. You should always be honest with your attorney in discussions. Anything you tell him or her is privileged and can only be discussed openly in very few situations.
The benefits of telling your attorney the truth are plentiful. For starters, being honest with your attorney helps build a better trusting relationship and ultimately better representation. Attorneys deal with clients on a regular basis and can generally tell when a person is holding back or outright lying. This can make an attorney uneasy and in turn not trust you. Second, knowing the truth of your guilt or innocence can help an attorney to better understand your situation better. And help provide a better defense or get a better plea offer from the state. Finally, being honest in all aspects of a case helps to avoid surprises later on down the road that could be detrimental to your defense.
There is really only one foreseeable drawback to being totally honest with your attorney. If you wish to testify on your own behalf and the attorney believes you are likely to fabricate something on the stand, he may have to withdraw from your case. This only happens in extreme circumstances however. If you want to testify untruthfully on the stand, and your attorney is telling you not to testify, then it is likely the relationship broke down much earlier.