Hello Bluelight,
Apologies for the really long post, however this OP is facing an important decision. I am a new user, so I understand that you may want to take my opinion with a dash of salt. However I hope some of this information might help you to think about what you want to research further and about the questions you might want to ask your doctor(s).
In terms of being anaesthetised, I don't think you have much to worry about as anaesthesia is achieved using a multi-modal approach. This means that more than one type of receptor is targeted, not just your opioid receptors.
To anaesthetise a person, the anaesthetist (or anaesthesiologist in the U.S.) will inject you with an induction agent, typically propofol or thiopentone (I think this is called sodium pentothal in the U.S. - please correct me if not). These drugs target receptors other than the opioid receptors (probably GABA, although this is still not certain). In addition to this, a strong opioid, such as fentanyl, will usually be given. If the anaesthetist thinks you are not asleep enough after the first lot of drugs are given, then he/she will give you more until you are at the required depth, i.e. unresponsive to painful stimulation.
Information about how much induction agent(s) were needed to get you to sleep will be taken into account when deciding how much maintenance agent should be used to keep you asleep. So if a load of propofol and fentanyl were needed to anaesthetise you, then the anaesthetist will know that a larger dose maintenance agent will be needed in order to keep you asleep.
The most common method of maintaining anaesthesia is to continuously administer a vapour, such as isoflurane or sevoflurane, via the patient's breathing tube. These vapours have a rapid 'onset' and 'offset', which means they can be titrated (i.e. increased or decreased) against the patient's response very quickly and accurately. So if the anaesthetist thinks that you are not in a deep enough 'sleep' then the amount of vapour you are breathing can be increased very quickly in order to get you to the required depth. Sometimes, in special circumstances, a continuous infusion of propofol is used instead of a gas, however the principle of rapid titration against response is the same. Usually further doses of an opioid, such as fentanyl, will be given regularly or as a continuous infusion during surgery. There are also other drugs that can be given to keep you at the required depth of anaesthesia such as ketamine, clonidine and benzodiazepines (such as midazolam or lorazepam).
What I am trying to get across is that your anaesthetist will use other drugs alongside opioids and will keep a very tight control of your depth of anaesthesia. He/she will be able to respond very quickly to any signs that you are not at the required level of unconsciousness before you even approach the point where you would become aware or awake. This is called 'anaesthesia awareness' and is a very rare event.
If you are going to have any problems then I think they will occur during the post-operative period and will be caused by the fact that your high tolerance could mean that you need a greater dose of opioid drug than the average person in order to achieve adequate pain relief. Luckily for you, there exist many other drugs that can be used alongside opioids in order to boost their pain relieving effectiveness. This is usually known as drug 'synergy' and means that the action of both drugs when given together is greater than it would be if they were given separately (or 'greater than the sum of their parts').
Another technique that would be excellent for you would be 'Patient Controlled Analgesia', which allows you to control how much opioid pain killer you receive according to the level of pain you are experiencing. Wikipedia has a great article on this, just search 'Patient Controlled Analgesia'.
On the subject of whether you should tell your doctor(s) about your increased opioid tolerance - this is a difficult one and may depend upon how understanding they are. On the one hand, if you do tell them, then they will hopefully be able to take this into account and change your medication appropriately. However, if you do not have an understanding anaesthetist then you may be labelled as a 'drug seeker' and denied adequate pain relief. A decision such as this is obviously yours alone to make. However I was in a similar situation a few years ago when I required an emergency repair of a fractured clavicle. I opted not to tell any of the doctors and nurses about my opiate tolerance and everything worked out fine. However this decision was kind of forced upon me as I was a member of staff at the hospital, so I wasn't really in a position to risk my professional registration by admitting to being an opiate addict.
I apologise for the lack of references, however the information here is meant to help you decide what you want to research further and what you want to discuss with your doctor. I'm happy to point you in the direction of some reliable sources if you need more information.