Yes Iran would be formidable to invade but they would be defeated by the combined might of the right alliance of ME powers such as Egypt,Israel,Jordan,UAE, etc. The distance would not be a problem for Egypt to stage its military in Kuwait or Saudi Arabia. The telling battle for the war would be the air and bombing battle. Once the allies have control of the air and knock out Iran's missile capability they can then send in their invasion force. If Israel is involved most of the Iranian missile capability will be destroyed within 3 weeks. If they aren't involved it could take months depending on the level of tech the allied air forces possess. I'm sure Western intel assets would provide info for the alliance.
No doubt the alliance will sustain damage from Iran's missile capability. Oil infrastructure will be targeted and prices will sky rocket,markets will collapse and economies hurt. So these would have to be a priority target. Probably taken out in a surprise or tech attack. So no one will walk away unscathed from a war. Israel would surely be attacked and have to fight in Lebanon, Syria. Iraq would probably become involved
A war would likely involve most of the ME nations. Its like I said its the door no one wants to see opened.
I can't remember how long I've read about the coming war with Iran which would engulf the ME unless something was done to curtail Iran's actions.