"Pulsatingly" is a perfectly reasonable coinage that fulfils all expectations of how the word is formed. Spellchecks won't like it, but that's par for the course. Use it in most places and no-one would bat an eyelid.
"It writhed pulsatingly" is a slightly icky image, but not in any way awkward. "Pulsatingly pumping into", on the other hand, is a little awkward, but really depends on context. In, shall we say, a certain type of fiction, it wouldn't go particularly amiss. It is pleasingly alliterative, as well as an example of purple prose (which is similarly alliterative, good coincidence). In case you're not familiar with the concept (and plenty of places online will explain it), it basically refers to excessively florid writing with far more description than necessary, making use of relatively esoteric word choices (like using 'cerulean' rather than 'blue').
Depending on what you're writing, I'd give it anything for 0.5/10 to 6/10.
Oh, and just don't use it in anything which isn't narrative. Fiction, or narrative non-fiction, sure. And poetry, that could be fine, though I foresee difficulty fitting it to metre. Don't include it in a science report.