SPD *can* be "outgrown" (eventually proper neural pathways develop, naturally or with assistance) ... or it can stick around. Various therapies do actually "cure" it, and OT can help with that if your Occupational Therapist is on the up-and-up about exercises that will help the child's brain wire (or re-wire) properly, and not simply trying to get the child to behave "normally" for the convenience of those around them. (I imagine most OTs are on the up and up. I've also watched some state regs in the school system try to pin their OTs to the school's priorities.)
All the different aspects of your child's particular SPD need to be examined, in addition to the overall picture.
One of my children had very clear SPD (although I had already stepped out of the allopathic medical world by then, so there is nowhere an official diagnosis, which has been a pain in my butt since then). I figured it out when he was about 14 months old; he couldn't process language under stress, he didn't seem to know where his body was precisely as he careened through the house, and he didn't have any understanding of cause and effect (this isn't SPD, itself, but was somehow wound up in the language and physical issues). I have a brother on the autism spectrum (often related to SPD issues) and some other adults I know who still have SPD issues with sound, so it was the sound levels/language thing that tipped me off. He also hadn't properly crawled until very late, using a commando crawl ... again, related to not having the body 'hooked up' correctly in the brain. (Another child of mine always tucked one foot under when he crawled, which is a sign that one half of the process isn't firing. I was very relieved that a few months after he learned to walk he spent a lot of time crawling again--but properly this time :). Yay!)
Luckily soon after I figured out my child had SPD (and was reading up on how to help him along/deal with this), I toured a Waldorf kindergarten, and instinctively knew that this was exactly the kind of environment my child needed in order to have mental "space" to process and get his brain wired up: low light, quiet, gentle stories, sing-song and singing (*really* helps with language acquisition for kids who aren't quick at it), lots of natural-fiber/wooden toys (so they get real weight and textures to program their senses with, instead of super-light plastic in over-stimulating colors). This environment is of course great for all kids before gradeschool, developmentally, but it was vital for this child (and there was no way my messy, noisy house was ever going to provide it!!). So we ponied up for that year and then leaped into a new public (read: free!) Waldorf-methods charter school.
I am not recommending Waldorf as the answer to all SPD problems--although we were particularly lucky that one of our teachers had an additional degree in sensory issues for young children, and all Waldorf teachers are trained to consider the right-brain-left-brain crosswiring and work from an assumption that we need to live into our physical bodies first before we have a foundation for healthy brain growth (learning), so it's not a bad answer to consider. What I liked about it was that it was so holistic ... the entire environment was designed specifically to support children rather than demand developmentally inappropriate things of them. That said, I have heard that Waldorf doesn't always cope well with a child they haven't reached when they are young. Some schools end up telling parents they need to send their child to this or that specific one-place-in-the-nation therapy (there's one involving lights and sounds, for instance, which I'm pretty sure probably does work to directly reprogram pieces of the brain but it is waaaayyyy out there on the "woo woo" scale for what Americans are generally willing to consider legitimate).
Even with all that, my child was still doing so much processing at this school that he regularly fell asleep or overloaded (and acted out, usually by simply refusing to move) before the half-day was out ... but these episodes grew fewer and farther between over the year. It's now a few years later and people who didn't know him before he was at the charter school are surprised to hear me say he was deeply SPD ... I know he was still working through SPD issues when he arrived, but by that time his behaviors were on the troublesome side of "normal" rather than clearly "SPD" ... and he's pretty much caught up to his classmates now :).
Find an OT you trust who will listen to your specific experiences and home needs; good OT can't hurt. Read up. Trust yourself. See how long it takes you to really feel like you understand the term "Proprioceptive" ;). (It's about understanding one's body in space. When you can use it comfortably in conversation, you'll know you've got a handle on what's happening ;)!)
Good luck and God's speed, Momma :).