Not easily. You could try to target it with CSS attribute selectors… maybe.
A code block will look like this:
<p>
<code>some code</code>
</p>
and inline code looks like this:
<p>
"Lorem ipsum "
<code>some code</code>
" dolor sit amet."
</p>
The difference is in the quote marks.
But, wouldn’t you want to be consistent and have both with the same background?