Furthermore, a typical risk profile does not provide breakdowns of option values individually in terms of volatility, interest cost, and intrinsic value.
Ah, I understand... Since I come from a different world (rates), a strangle to me is always with both options OTM (I guess that's what you call an OTM strangle). To me, there's no such thing as an ITM strangle, as there's never any point in trading anything of the sort. Obviously, ITM strangle = OTM strangle follows trivially from put-call parity. Good to learn how stock option peeps do their thang...
I'm not completely sure. However, for a value graph of straddle/ strangle options, the component values for call and put individually are quite different and of different shapes. Say, ITM puts lose their time value faster than ITM calls do, typically. I may be wrong.
On page 411 of McMillan on Options, it says about straddles, "Options lose time value premium as they become ITM options, and ITM puts lose their time value faster than ITM calls do. "
Your statement is not precise. If you mean it in general, then the answer is No (despite you may have been told).
Would you mind to explain why "No"? What do you mean "Precise"? Do you mean the word "equivalent" used in options is Not precise enough? Perhaps a synthetic call is equivalent to a call, but it is Not actually a call. Right?
Instead of running people and yourself around in circles, get hold of a risk graph program and prove yourself wrong. Pick an implied volatility so that all options are based on the same IV. Input a long OTM strangle against a short ITM strangle (same month and strikes). Graph the psoition. You'll see that the risk graph is a horizontal line at zero (or very close to zero if the was a few penny debit or credit due to rounding errors in the option pricing).