In the passage to follow, Paul explains why most of the Jews remained unsaved

Strictly speaking, there is no mention of salvation in the passage you quote. The passage deals with "righteousness" (δικαιοσύνη - dikaiosynē), not "salvation" (σωτηρία - sōtēria). They are not the same thing, though often conflated.

The KJV offers a much more literal translation of Romans 9:31-32, in my opinion:

But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness. Wherefore? Because they sought it not by faith, but as it were by the works of the law.

The ESV truncates the Greek to such an extent that a completely different meaning emerges:

But that Israel who pursued a law that would lead to righteousness did not succeed in reaching that law. Why? Because they did not pursue it by faith, but as if it were based on works.

"Faith" and "belief" are exactly the same word in Greek: πίστις (pistis). Romans 9:31-32 states directly, therefore, that Israel did not attain righteousness ("the law of righteousness") because they sought it through works of the law rather than through belief (πίστις).

The question remains as to whether Israel had any choice in doing this. The only possible basis for supposing Israel did not have any choice would be a fairly narrow interpretation of Romans 8:28-29:

For whom he did foreknow, he also did predestinate to be conformed to the image of his Son, that he might be the firstborn among many brethren. Moreover whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified.

"Predestinate" (προορίζω - proorizō) has been interpreted to mean "decide beforehand" (e.g. Swanson, Dictionary of Biblical Languages with Semantic Domains: Greek (New Testament), but this doesn't seem to be the way the word was understand by Greeks in antiquity. Chrysostom (4th c.) comments on the passage, for example:

It is not the calling alone, but the purpose of those called too, that works the salvation. For the calling was not forced upon them, nor compulsory. All then were called, but all did not obey the call.^*

Thus, in answer to your question:

Can it conclusively be established, based on this verse and the surrounding context, that Israel had the capacity to believe and yet willfully chose not to?

I believe the answer is yes; but it requires interpreting the Greek in places in the fashion it was interpreted by certain Greek Church Fathers.

^{* Homily XV on Romans}

In the passage to follow, Paul explains why most of the Jews remained unsaved

Strictly speaking, there is no mention of salvation in the passage you quote. The passage deals with "righteousness" (δικαιοσύνη - dikaiosynē), not "salvation" (σωτηρία - sōtēria). They are not the same thing, though often conflated.

The KJV offers a much more literal translation of Romans 9:31-32, in my opinion:

But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness. Wherefore? Because they sought it not by faith, but as it were by the works of the law.

The ESV truncates the Greek to such an extent that a completely different meaning emerges:

But that Israel who pursued a law that would lead to righteousness did not succeed in reaching that law. Why? Because they did not pursue it by faith, but as if it were based on works.

"Faith" and "belief" are exactly the same word in Greek: πίστις (pistis). Romans 9:31-32 states directly, therefore, that Israel did not attain righteousness ("the law of righteousness") because they sought it through works of the law rather than through belief (πίστις).

The question remains as to whether Israel had any choice in doing this. The only possible basis for supposing Israel did not have any choice would be a fairly narrow interpretation of Romans 8:28-29:

For whom he did foreknow, he also did predestinate to be conformed to the image of his Son, that he might be the firstborn among many brethren. Moreover whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified.

"Predestinate" (προορίζω - proorizō) has been interpreted to mean "decide beforehand" (e.g. Swanson, Dictionary of Biblical Languages with Semantic Domains: Greek (New Testament), but this doesn't seem to be the way the word was understand by Greeks in antiquity. Chrysostom (4th c.) comments on the passage, for example:

It is not the calling alone, but the purpose of those called too, that works the salvation. For the calling was not forced upon them, nor compulsory. All then were called, but all did not obey the call.^*

Thus, in answer to your question:

Can it conclusively be established, based on this verse and the surrounding context, that Israel had the capacity to believe and yet willfully chose not to?

I believe the answer is yes; but it requires interpreting the Greek in places in the fashion it was interpreted by certain Greek Church Fathers.

^{* Homily XV on Romans}