I think you need to make the distinctions between bookkeeping, accounting and management accounting.
Depreciation is for accounting purposes calculated at the end of the year on your fixed assets and recorded in the P&L account.
There's nothing stopping you charging a 1/12 estimate of that figure in your monthly accounts so that for performance assessment you've got a reasonable idea of how the business is doing. There's nothing worse than getting to the end of the year and saying the accounts show I made £50K profit only to find the accountant's just wiped that down to nothing because of the year end adjustments for stock, depreciation, accruals etc.
Whatever you put through your books monthly for depreciation, as long as it's clearly documented between your balance sheet 'Depreciation charge for the year' account and your P+L Depreciation account is fine, your accountant can run the accurate calculation and balance the figures as needed.
The other way of reading your question, can you take depreciation into account in costing a project, yes, the same as you'd have a proportion of your fixed costs, rent, rates, light etc, attributed to any project costs.
How you'd account for those costs within your bookkeeping though and how you assess performance on a project are two different things. I'd tend to keep any assessment of a projects performance separate from your bookkeeping and accounts unless you've got a dedicated bookkeeper that can put the workload in to take each cost and assign it to the right P&L account and project cost centre.