The so-called tyranny of the rocket equation, which becomes clear by examining Tsiolkovsky rocket equation, defining maximum change in velocity $\Delta v$ as:
$$\Delta v = v_\text{e} \ln {\left(\frac{m_0}{m_1}\right)}$$
where $m_0$ is the wet mass, $m_1$ dry mass, and $v_\text{e}$ effective exhaust velocity of reaction mass, shows that:
Rockets are momentum machines. They spew gas out of a nozzle at high
velocity causing the nozzle and the rocket attached to it to move in
the opposite direction. Isaac Newton correctly defined the mathematics
for this exchange of momentum in 1687. Conservation of momentum
applied to a rocket was first done by Russian visionary and scientist
Konstantin Tsiolkovsky in 1903. All our rockets are governed by
Tsiolkovsky’s rocket equation.
This means that reaction mass that conventional rockets (chemical rockets, thermal rockets,...) need to carry with them, while necessary to achieve thrust ($\mathbf{T} = \frac{dm}{dt} {v}$) and with it movement in the opposite direction to their exhaust, directly following principles described in Newton's laws of motion, also increases their initial mass and with it impede total achievable $\Delta v$. And as you approach relativistic speeds, all that mass becomes heavier and requires even more energy to accelerate faster.
All this means that increasing rocket's mass by adding additional required systems or shielding mass to it directly lowers its performance. It will accelerate slower, and reach its destination later. As far as exposure to cosmic rays and solar high energy proton flux is concerned, radiation dose is governed by the duration of exposure, its intensity (proximity to its source), and a few other, more-or-less invariable factors we can't control with rocket systems alone, like our body density.
There is not much we can do to block the most energetic chargeless particles in cosmic rays (such as neutrinos, and if I remember correctly, we'd need many light-years thick block of led to block half of them). As for smaller eV radiation, short of reducing exposure time, there are ways to deflect most charged particles with a dipole magnetic field, and/or blocking lower energy mass particles by shielding mass, where water (or water ice) is fairly good at that (see another, also relevant answer).
So it makes perfect sense to decrease exposure time, accelerate fast away while in the inner Solar system (proximity to the Sun), decelerate even faster at your destination since the rocket is by then lighter, and shorten total trip time. So yes, reusing any rocket's mass for multiple purposes makes perfect sense, and even if that mass is a consumable, it would be required as reaction mass anyway, so why not use it as a shielding mass for biological
shield as well? Since it's water, you'd likely use it for other purposes as well, such as a source of oxygen, potable water, coolant,... and you can recycle most of that, so there would always be at least some available and not all of it consumed as reaction mass.
However, unless that's required by the rocket's design, forward shield only makes sense if the source of the most of radiation you'd like to block is coming from in front of the rocket, meaning you're likely travelling at a significant fraction of the speed of light already (at which point a collision with a grain of dust might be catastrophic, due to $E_\text{k} =(m c^2)/(\sqrt{1 - v^2/c^2}) - mc^2$ with $E_\text{k}\approx\tfrac{1}{2} mv^2$ when $v$ is much smaller than $c$, see explanation here), are faster than harmful matter from behind you, and you're for some reason not concerned by the impacts orthogonal to your vector of travel, otherwise you'd likely want to shield the crew module all around, not merely from in front of the ship. Like for example in this Conceptual Design of Crew Exploration Lander for Asteroid Ceres and Saturn Moons Rhea and Iapetus (PDF):
So TL;DR - It makes perfect sense to reuse as much of the vehicle's reaction mass for multiple purposes, including increasing protection from harmful radiation and impacting with smaller debris while in areas and at relative velocities where it's more likely to happen and total kinetic energy discharged on impact can be shielded against. It will also decrease total travel time, further lowering exposure time to harmful radiation. But solely forward shielding likely doesn't make much sense, if this bioshield mass could instead be distributed all around the crew module. As the vehicle increases velocity and if that on itself changes direction of harmful radiation and likelihood of impact at ram-facing side of the craft, then part of the threat mitigation could also be gradual use of bioshield mass from where it's less needed first.
