Short answer - not darn likely, due to tearout sequence, and because showering and getting water from dripping and wet feet on subfloor before finish flooring is completed is likely to damage the new flooring level and bond.
A simple tub/shower tearout and tub/surround install might get done in 3-5 work days under ideal conditions. Sorry, but if subfloor needs replacement, this has to be torn out first because you have to chase down the water damage requiring subfloor replacement, and it extends in under the tub so shower/bath will be out of service from day one to basically end of job. Presume this subfloor replacement is due to water damage, so damage probably extends in under tub area. Either way new shower will require new subfloor in that area too, so the order of work is roughly this: vanity/cabinets/toilet need to be removed, tub/shower and flooring and subfloor tearout has to be done, any subfloor structural repair (floor joists) done, then any plumbing rework (and electrical if any) repaired or roughed in, new tub installed, water resistant backing board put on walls (sometimes vice-versa on these two depending on installer and panel design), then the wall panels put up, shower/tub hardware and shower doors installed, then finish flooring installed, toilet and vanity and cabinets reinstalled, and finally any baseboard/toekick installed and touchup painting done. Depending on selection of type of flooring and such may be a little variation in order, especially in whether vanity/cabinets/toilet go in before or after finish flooring, but this should give you an idea of the order.
In an ideal world, with absolutely ALL materials on-site up-front before they start demo, an excellent general contractor could get this done in about 4 work days, assuming subfloor damage does not extend under adjacent walls and no structural repairs are needed to subfloor - just sheathing replacement. Real world - not less than two weeks if you are real lucky and all subs show up when expected, likely closer to a month or so. If you get a contractor from hell (see Shelley Long and Tom Hanks movie The Money Pit or several prior questions about unfinished bathroom remodels on this website for samples), months and months. Also, if floor structural members are seriously damaged by long-term water leakage, this can potentially increase both duration and cost by double or more.
If I were you, if you are looking at upgrading another bathroom with a shower and this one is still usable and safe (i.e. not falling through floor) I would get that done first to give you a finished bathroom, then tackle this one. Otherwise, get a month to month family membership at a fitness club near home or work and take up a new year's fitness routine and shower after your workout each day. Or get real used to sponge baths. I have even seen people get the contractor to set up a temporary set of pipes and showerhead and 360 degree wrap-around shower curtain over the floor drain in the basement or garage (leaving car outside, of course) to have a shower available during their only 3/4 or full bathroom remodel. I have also seen people rent a small RV with shower - not too expensive as a rule in winter, though have to keep heated and will have to drive to the dump station fairly frequently if used daily for showers by several people.
Maybe Don or Todd or Ben orone of the other contractors who provide responses on this forum will jump in here with their thoughts on time to complete, so you have several opinions.