In principle, yes. In practice, for small quantities of salt, no. This is a very simple experiment to perform.

If you're interested in the theory, this is mostly chemistry. The elevation in boiling temperature caused by adding the salt [can be expressed as][1]:
$$\Delta T=Kbi$$
where $K\approx 0.5 \,\mathrm{K \,kg \,mol^{-1}}$ for water is called the ebullioscopic constant, $i\approx 2$ for salt (in water $\mathrm{NaCl}$ dissociates into two) and $b$ is the molality, that is the number of moles of salt per mass of water.

Heat is absorbed according to the law
$$Q = M C (T_f-T_i)$$
where $M$ is the mass, $C$ is the heat capacity, $T_i$ and $T_f$ the initial and final temperature. Notice that adding salt lowers the heat capacity of the solution. The exact behaviour is complicated. However, [here][2] we can find the heat capacity of the solution as a function of concentration (by mass). 

Let $m_w$ be the mass of the water, $m_s$ be the mass of salt. Let $C_w \approx 4200 \mathrm{J kg^{-1} K^{-1}}$ be the heat capacity of water only, and $C_{sol}$ the heat capacity of the solution. The heat absorbed by water only to boil is:
$$Q_1 = m_w C_w (T_0-T_i)$$
The solution has more mass, and needs to reach a higher temperature so it needs an amount of heat equal to: 
$$Q_2 = (m_w+m_s) C_{sol} (T_0+\Delta T-T_i)$$

Assuming a constant heat source, the time it takes to heat to a certain temperature is proportional to the amount of heat needed.

So if $t_1$ is the time it takes for water only to boil, and $t_2$ is the time it takes for water + salt to boil, the ratio of these two is:
$$\frac{t_2}{t_1}=\frac{Q_2}{Q_1}=\frac{C_w}{C_s}\left(1 + \frac{m_s}{m_w}\right)\left(1+ \frac{\Delta T}{T_0-T_i}\right)$$

So now suppose we use $1\mathrm{kg}$ of water and start at $T_i=20^\circ \mathrm{C}$. Say we add $10 \mathrm{g}$ of salt; we can use [this online calculator][3] to obtain the number of moles, which in this case is $0.17\mathrm{mol}$. The change in $C$ and $m$ is negligible, so we get:
$$\frac{t_2}{t_1}=1.002$$
so it takes about $2\%$ more time if you add the salt.

Say instead we add $0.2\mathrm{kg}$ of salt, corresponding to about $3.4$ moles. Then according to the source above the heat capacity of the solution is going to be $C_{sol}\approx 3300\mathrm{J kg^{-1} K^{-1}}$. Therefore we get:

$$\frac{t_2}{t_1}\approx \frac{4200}{3400} \times 1.2 \times \frac{3.4}{80} \approx 1.06$$

which is only $6\%$ more time. So even when substantial amounts of salt are introduced the change is not much.

  [1]: https://en.wikipedia.org/wiki/Boiling-point_elevation
  [2]: https://www.engineeringtoolbox.com/sodium-chloride-water-d_1187.html
  [3]: https://www.convertunits.com/from/moles+NaCl/to/grams