Verbs with different tenses and different complements joined by "and"

Is it grammatically incorrect to join two verbs with different tenses?

E.g., "This project hoped to and has potentially succeeded in producing one such possible framework..."

Here "hoped to" refers to the original intent when beginning the project and "has succeeded in" refers to the results of the project now that it is near completion.

Yes, a coordination of verb phrases with unlike tenses is perfectly alright.

This project hoped to succeed. This project has potentially succeeded.

In your example, however, the verbs take different complements: hoped to takes bare infinitive succeed, whereas has takes past participle succeeded.

I'd say you've got a faulty coordination on your hands. On the other hand, as it still reads acceptably well, we might also take the missing complement to hope to ____ as omitted and understood through context.

There are two options for fixing the coordination:

...hoped to succeed... or ...hoped to produce...

It is absolutely grammatical to use different tenses joined by 'and'. "I can and will get the project done." or "I don't understand Postmodernism. Never did and never will." These sentence condense parallel notions into one, but because they refer to the same ideas the meaning is clear.