Learn English – Shall, third person singular, archaic form

The answer to the OP's question is: 'yes'. Mostly. The only English verb which differs from its plain form outside of the third person, is the verb BE. The verb BE is usually an auxiliary verb.

However, the verb BE can also be regarded as a lexical verb in sentences such as:

• If you don't be careful ...

Notice that the sentence above uses DO as a dummy auxiliary even though BE is present. Because of this there might possibly be cases where it is impossible to distinguish between BE as a lexical or auxiliary verb. However, I know of no such cases. Lexical BE rarely if ever rears it's head as a tensed verb. Arguably the positive polarity version of the phrase above is:

• If you be careful

Here we are still using the plain form of the verb, not the present tense. There is a strong case therefore that tensed BE is always an auxiliary. This would mean that there are no exceptions to this rule.

However, there is one more issue that might put a spanner in the works here. The verbs BEWARE and USED have no present tense form in current usage. BEWARE is only ever used in the plain form because it only occurs in imperative constructions. The verb USED as in I used to smoke, is only used in the past tense. It could be argued, therefore, that these verbs do not have any present tense form that is identical to the base or plain form.

You can read more about lexical versus auxiliary BE in the reference grammar The Cambridge Grammar of the English Language by Huddleston & Pullum, 2002.

Shall is an auxiliary verb, so its conjugation follows the rules of shall/will/can/may/should/would/could/might and is different from regular verbs. The only change from the base form is for second person singular:

I shall, thou shalt, he shall, we/you/they shall.

(And you could have figured this out for yourself; look in Shakespeare, e.g. That henceforth he shall trouble us no more.)

And the subjunctive be is the same for all subjects. So:

He shall get kings, though he be none.