Can hydrogen on platinum reduce carboxylic acids and esters?
This is based off my memory, as far as I can remember what my teacher taught me.

Note, instead of $\ce{Pt}$, you can go for $\ce{Ni}$ (or Raney Nickel) or even $\ce{Pd}$ as a catalyst.
Functional groups such as acid halide, cyanide, nitro, aldehyde, ketone, alkene, and alkyne are easily reduced by $\ce{H2/Ni}$.  Some other groups can be reduced with $\ce{H2/Ni}$ as well, but if someone's asking you a question in an exam, they want you to refer to the list of groups which are easily reduced (more in the reactivity order below).  So the answer in your case would be a no.
Next, here's a reactivity order:
First, the groups which are easily reduced:
$$\begin{align} \text{acid halide} &gt; \ce{R-C#C-R} &gt; \ce{R-C=C-R} &gt; \ce{R-CHO} &gt; \\ &amp;\text{ketone}&gt;  \ce{R-CN} &gt; \ce{R-NO2} &gt; \ldots \end{align}$$
Then the groups that are reduced only with difficulty:
$$ \ldots &gt; \ce{R-X} &gt; \text{benzene} &gt; \ce{R-COOH} &gt; \text{amide} &gt; \text{ester} &gt; \text{acid anhydride}$$
$\ce{R-X}$ would require temperatures around $\pu{50^\circ C}$, benzene would require a temperature of about $\pu{100^\circ C}$ and groups from carboxylic acid to acid anhydride would require temperatures around $200-\pu{250^\circ C}$.