Learn German: Ich komme jedenfalls pünktlich. - I will be on time in any case.

They are largely interchangeable and both mean "in any case" or "definitely". However, jedenfalls can sometimes carry a slight tone of "regardless of what happens" or "whatever anyone else does". If the speaker's friends are running late, they might say this to mean, "Well, I am arriving on time, anyway."

The English translation says "I will be on time", but the German uses komme (come). Can I say Ich bin jedenfalls pünktlich?

Yes, Ich bin jedenfalls pünktlich is perfectly fine. But Germans frequently use pünktlich kommen (literally "to come punctually") to describe arriving on time, whereas English speakers naturally default to the verb "to be".

Why doesn't the sentence use the future tense Ich werde jedenfalls pünktlich kommen?

German heavily prefers the present tense for future events when the context makes the timeline clear. While the future tense with werden wouldn't be wrong here, it often sounds unnecessarily formal or comes across like a solemn, dramatic promise rather than a standard everyday statement.

Could jedenfalls be translated as "at least" here, similar to wenigstens?