Things I'd consider
1)Why play a site with raked rebuys? Unless u think their will be overlay or some other incentive to play their are sites that don't charge rebuy rake.
2)Doubling your chips won't double your equity. Particularly if you paid rake.
3) Players - Who is at the table? Are they strong or week? Do u like your seat? Has the strongest player got position on you or has the donkey won an all in and is eager to give the chips back.
4)Add on- What cost is the add on?How many chips? How many BB will that be?
5)- What is the playability of the stack I'm buying? What is the speed of the Torni?
6) Who else at the table has taken a rebuy?

As for your examples I can't think of a reason why a rebuys would be more or less profitable in a satellite of a regular torment? Would be interested if anyone could find a reason.

All good points.

The add on on almost all sites is a no brainer. As its normally double the chips for the same buy in.

When I first started playing years ago rebuys were never raked in mtts. It was the accepted logic by al good regs to rebuy straight away.

Stars rebuys for example - on average I still see 2 or so players take the rebuy straight away. I no longer do. Was just wondering if there still stuck in the old way of thinking.

Ill detail the nuanced situation I'm facing is below. It touches on the subject of overlay that you bought up

There's a site in the UK that runs satellites online twice a week to there flagship live events

5 x £1110 seats GTD. Total prize pool £5560. I like playing these as the fields are super soft and I have no problem selling my seats at the live events for almost face value.

Its a £110 initial buy in ( the 10 is rake ) in for 3000 chips

1 optional rebuy for 3000 chips @ £110 (10 is rake again)

1 add on for 5000 Chips @ £110 ( this bit is a no brainer )

These sats regularly overlay. Lets say on average its regularly in the region of £1800 to £500. Great value.

Now given all that info. What should my approach be on taking the optional raked rebuy straight away?

In short am I decreasing or increasing my EV by taking it?

Further i info you have to be below starting stack to rebuy. If I see a couple of super fish on the table double early, I often take the rebuy if I can Or even donk of a couple of hundred chips to take it. As these players are so bad I want to match there stack.

My 2 cents worth...
Anything that is tagged as a "no brainer" the person tagging it has not thought about it enough.

If the add-on does not give you a significant boost to your stack, i.e. if you are already a significant stack there is no need to add-on as it does not directly equate to EV.

The same in many regards with the rebuy, how soft is the field? If you can double up early against a fish why spend an extra $110 when the equity you hold can already be worth 1.2 - 1.5 to 1 anyway against said fish. Getting to the business end of the tournament having only spent $110 would significantly increase your overall ROI, however, if the field is really tough the numbers change and the rebuy can become a significant negative ROI drain and the whole equation changes, only you can fully assess the situation but you must remove all "no brainers" from your thinking first.

Good luck
3p out

In the specific situation u are outlining it sounds like you are only allowed 1 rebuy? If that's the case I would be inclined to avoide the rebuy because if I take it and get eliminated I'm going to lose out on the overlay.