Short answer is yes. The bathtub has a rim that goes up and under the tile and at least the first few rows of tile will have to be removed. There is a chance that the floor tile can be preserved but most likely it will be damaged when the tub comes out.
Usually standard tubs are built in with little tolerance and the only way to remove them is to remove the surrounding tile. Another way to deal with these tight tolerances is to saw the tub into half or at least create a section in the middle that can be removed to provide some relief for the tub to come out. Old porcelain tubs can be busted apart with a sledgehammer and then hauled off in pieces.
Tubs have their rim up under the tile so water can’t directly flow into the walls. This makes most tile surrounds not salvageable when the tub comes out. DIY bathtub refinishing becomes an option if the tile is to be saved. When it comes to bathtub refinishing you have the choice of professional refinishing or do-it-yourself refinishing kits.
More information about the bathtub refinishing process can be found here: How To Refinish A Bathtub
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