Yeah, I think so.
I went and looked up the datasheet.
+V - 1.9V is the "typical" value. What that word means in a datasheet is "We kinda think most of them will work like this, but no guarantees." The words min(imum) and max(imum) mean "We'll give your money back if they don't do this and we can't figure out how you could have been applying them wrong to make that be that way."
The actual limits they will guarantee are +V -2.6V - that word "max" appears next to that one.
So if you're using a 9.0V supply, biased at 4.50V, you may only count on the thing working right if you use a signal less than what moves the inputs up to 9.0-2.6 = 6.4V. From your bias point, that's 1.9V peak. Get over that and... well, they don't say what will happen.
That's another thing to read in a datasheet. What do they NOT say. The datasheet doesn't talk about what happens when you exceed the positive input common mode range. It used to be that opamps pushed past Vicm went to the nearest power supply rail and latched there, pulling the power supply through the chip. Some of them went into SCR latchup which meant that by the time you got the power supply turned off, you had a smoking crater there. Newer opamps are better behaved, but since the datasheet doesn't say it, they don't guarantee what happens when you go there.
The moral of the story is - don't go there.