Could a bad tie rod prevent alignment?

No.   Anyone knows they will not do an alignment on a car with bad tires, warped disks, loose drive shafts, bad tie rods and bad steering connects.  If they do, they are automatically at fault for future problems and accidents.  They ain't stupid.

Yes.. If the tie rod is bad an alignment will not hold.  Get a second opinion on the tie rod. If your car is pulling to one side or the other, or your front tread is not wearing out evenly then you need the alignment. 

If your car is starting to get a lot of miles it is not uncommon for a tie rod to go bad. Its an important moving part of your vehicle, if it breaks while you are at high way speed it could kill you. On some models of cars the tie rod ends need proper lubrication to keep from going bad. So the issue is not make believe.

Contrary to what many people say, most shops do not put  out coupons to rip people off, they just want a chance to earn your business, get a second opinion and then go back and use your coupon and get your car fixed.

Well, usually when they put out a coupon for a service that is much lower than the norm, they likely are selling a lot of "junk" that mysteriously needs to be replaced before you get your bargain rate alignment in this case. So, a $99 alignment turns into a $500 alignment. 

I'd take it to a respectable shop that isn't handing out coupons and get a free second opinion. They can put it up on the rack and move things around to judge what's loose and what's not. 

Never heard of an inner tie rod wearing out. The outer tie rods usually are what wears out first and that's after maybe 20 years or 100K miles on bumpy roads. Or it wasn't lubricated when the car had an oil service or it has a sealed tie rod that isn't greaseable at regular intervals.

If you hear the same story from another shop that has no knowledge of the cars history elsewhere, then it might actually be true that it needs an inner tie rod. If it is in fact "worn out" or there's too much play in it, then yes you will need to replace it before doing the alignment. Make sure your best tires are on the front end before they do the alignment. 

Yes, the auto shop is correct. You being told you need a inner tie rod means it has excessive wear to the point that an alignment cannot be done properly.

Short answer is YES.  You are driving a PoS for a vehicle.  There is always other shops you can go to for an estimate on the cost.  Go to 3 different shops unrelated to each other (in other words not chain shops) and see what their price is and then choose who you gonna go to? basing on the price of the job.  That is how we shop.

Generally worn tie rods means the rubber bush has perished leading to some unintended movement around it.

A lot of these offers are sprats to catch a mackerel .

You can't do an alignment with a bad tie rod end. Most tie rod ends cost under $50. You can replace it yourself in 20 minutes. Watch a youtube video to see how it's done.

Yes, Thomas, the parts that hold the wheels in place are somewhat important to alignment and there is no point in paying to have the front end aligned if the parts are worn.

as there is movement in the joint where would like the play when he adjusts it?

Its not going to be correct . What a safe car you drive where there is one bad joint there will be more. 

They could do it, but since the part they are adjusting is bad, it would not hold.  It would just go back out of alignment within a couple of days.  It also would increase the odds that, by putting the additional tension on the tie rod, it could break.  At that point you would have no control over steering the car and would be putting you life at risk.  If the tie rod is bad, you need to get it replaced before that happens.  (And it will.)  When they replace the tie rod they will have to align the car then. so any money you spend getting it aligned before that is done is a waste.

If you are unsure about the work, get a second opinion before having it done.