Does he need to confer with his client?
Attorneys have a model code of professional conduct, by which they have to abide or be sanctioned by their state bar - which can be disbarment. The relevant rules for offers are 1.2 and 1.4:
1.2 (a) Subject to paragraphs (c) and (d), a lawyer shall abide by a client's decisions concerning the objectives of representation and, as required by Rule 1.4, shall consult with the client as to the means by which they are to be pursued. A lawyer may take such action on behalf of the client as is impliedly authorized to carry out the representation. A lawyer shall abide by a client's decision whether to settle a matter. [...]
1.4 (a) A lawyer shall:
(1) promptly inform the client of any decision or circumstance with respect to which the client's informed consent, as defined in Rule 1.0(e), is required by these Rules;
(2) reasonably consult with the client about the means by which the client's objectives are to be accomplished;
(3) keep the client reasonably informed about the status of the matter;
(4) promptly comply with reasonable requests for information; and
(5) consult with the client about any relevant limitation on the lawyer's conduct when the lawyer knows that the client expects assistance not permitted by the Rules of Professional Conduct or other law.
1.0 (e) "Informed consent" denotes the agreement by a person to a proposed course of conduct after the lawyer has communicated adequate information and explanation about the material risks of and reasonably available alternatives to the proposed course of conduct.
In this sentence, you need to look carefully at shall consult with the client as to the means by wich they are to be pursued. and he has to make sure that his client gets the informed consent. This means unless he is given the direct order to accept or deny something in advance, he not only shall not accept it, he has to inform his client of the offer and inform him about consequences.
For example, in a settlement discussion, the client says "Don't bother me with settlement offers of less than 10000 dollars." This would be a clear order that doesn't require the attorney to consult the client about the offer to deny a too low one, but he still needs to inform their client that the offer was given by the other side.
Can he bind his client?
An Attorney is paid to act on behalf of his client. As such, he can be tasked to give the ok or denial of his client to things offered to him. As I have shown above, he should discuss any such action with his client, because he is their agent at that moment.
A good attorney will confer with the client and discuss what is acceptable or not before a conference and get any orders to do something or not do something in writing - both to secure himself (see above, disciplinary actions loom) and to make sure his client is in the loop.
However, grave misconduct of the attorney - accepting an offer against a direct order from the client - could lead to the acceptance of something getting voided.