Nope...PE tanks don't permeate
However, unless you put plugs in the fittings of tank you've removed, odor from inside the tank can escape...something that has misled more than one person into believing the tank had permeated. A poster here a year or so ago had pulled his tank out and put in his garage...nothing could convince him that the odor in the garage wasn't due to a permeated tank.
But it's very possible that odor from your permeated hoses, from the "primordial soup" than can live in bilges etc has attached itself to the outside of the tank..and to every surface the hoses pass through.
So once you've gotten everything out, buy some PureAyre
PureAyre ... Thoroughly clean your bilges and every area the hoses have passed through with detergent and water...let it all get dry....then put the PureAyre in a pump garden spray jug (MUCH easier to use than a trigger sprayer..the Roundup brand ones at Walmart cost about $15, but are really good quality) and "hose down" every surface, nook and cranny AND the outside of the tank. Don't rinse....just let it dry. And if you're in a mood to get rid of most of your closed-up-all-winter odors too, spray all your life jackets, foulies, cushions and other soft goods and put 'em all out in the sun to dry all day.
Now you're ready to re-install your system. Use Trident #148 for your head intake line and vent line if it's smaller than 1".
It's not necessarily true that all flexible hoses eventually permeate.... That used to be true, and most still do, but not all. Trident 101/102 have been on the market for more than 15 years without a single reported odor permeation failure...and Shields has just introduced a new hose--their Poly X--that they put a lifetime warranty on--and for their price/ft, it better last that long!
Btw, dog...water and holding tanks are all LDPE, not HD.