Advanced Custom Fields from Category – IF statement

You’re on the right track.

However your parameters for get_field() are incorrect in your example. The second value should be an ID or false (true is not valid):

// Incorrect. Uses 'true' as second parameter:
if ( get_field('logo_src', 'true', $taxonomy . '_' . $term_id ) ) {

Try this. Use get_field() to return the value of the field in your conditional statement argument. Use the_field() to print the value of the field:

$queried_object = get_queried_object();
$taxonomy       = $queried_object->taxonomy;
$term_id        = $queried_object->term_id;

if ( get_field( 'logo_src', $taxonomy . '_' . $term_id ) )
{
    the_field( 'logo_src', $taxonomy . '_' . $term_id );
}
else
{
    echo 'Nope.';
}