Learn French: Les paparazzis traquent tant la star qu'il n'y a pas d'intimité. - The paparazzi stalk the star so much that there is no privacy.

Yes! When describing the intensity of a verb, tant que and tellement que both mean "so much that" and are usually interchangeable. You could easily say traquent tellement la star qu'il.... Just remember that you cannot use très (very) here, because très is only used with adjectives and adverbs, never to modify a verb directly.

Why is tant placed before la star instead of after it?

In French, short adverbs that describe how an action is done usually go immediately after the conjugated verb. That is why tant directly follows traquent (stalk so much), rather than going after the direct object la star like it does in English.

Does intimité mean "intimacy" or "privacy"?

It means both! French doesn't have an exact equivalent for the English word "privacy." Instead, intimité is the standard word used to talk about your private life, personal space, or peace and quiet.

Why is it pas d'intimité instead of pas de l'intimité?

This is a great reminder of the negative rule: after a negative expression like il n'y a pas, indefinite and partitive articles (like un, une, du, de la) change to simply de (or d' before a vowel). If it were positive, you would say il y a de l'intimité (there is privacy), but in the negative it becomes il n'y a pas d'intimité.