That should do it.
This way you will be able to justify your offer based on the work that will be required to make the home livable.
And no, the bank won't pay for an inspection.
If you have a inspection addendum as part of the purchase agreement and you did find issues after inspection, you could either cancel the deal or request a cut on the price of the home. But as bank owned homes are sold 'as is' and are supposedly priced with condition in mind, there's no guarantee that they will either cut the price or make any necessary repairs. This is the risk when making an offer on bank owned and short sale homes.
The house is being sold 'as is' for a reason. The bank will not pay for your inspection - before or after you submit an offer. Buyers usually pay for the home inspection no matter what type of sale it is (bank owned, short sale, standard). Keep in mind the current list price may already reflect the items you are aware of and therefore a lower offer may not be accepted by the bank. Also, the bank may not 'allow' you to do an inspection before submitting an offer - your Realtor would need to check with the Listing Agent. Have your Realtor do a Comparative Market Analysis (CMA) on the property (if they have not already done one for you) using SOLD comps within a 1 mile radius of the property (the closer, the better) that have SOLD within the last 3 months. This will give you current market value of the property.
We are in no rush, and have seen houses go fast. We would like this property but there are more chances like you say for the bank to say no to lowering the price. The taxes are also very high, so if we get outbid, it wasn't meant to be. In a market as we have it, where things may even get worse, I am in no rush and we have watched it for over 4 years before actually looking at homes. We don't want to run into something that we can regret buying. Caution before everything.
You would have to request this with the Seller, through his Agent.
I have seen these General Inspections run $300 to $500.
Do not expect the SELLER or the Bank to pay for this; and if it came out negative, and if you chose not to buy the house, do not expect to lay it off on them.
This is YOUR thing, and YOU are choosing to do it this unconventional way.
You will probably find that the Seller knows about the problems, and have prices the house accordingly.