Hi Tony,
Welcome to BuddyDev and thank you for asking this.

There are multiple ways to do it.

1. Not that good but you will not need to touch any template file.
We can put the following in our bp-custom.php

/**
 * Check if user has uploaded cover
 * 
 * @param type $user_id
 * @return boolean
 */
function buddydev_user_has_uploaded_cover( $user_id ) {
	
	$cover_image = bp_attachments_get_attachment( 'url', array(
			'object_dir' => 'members',
			'item_id'    => $user_id,
		) );
	
	if( ! empty( $cover_image ) ) {
		return true;
	}
	
	return false;
}
/**
 * We use it to filter on 'bp_is_profile_cover_image_active' to enable/disable the cover display
 * 
 * @param type $enabled
 * @return boolean
 */
function buddydev_check_for_uploaded_cover( $enabled ) {
	
	if ( ! bp_is_user() ) {
		return $enabled;
	}
	
	$user_id = bp_displayed_user_id();
	
	if( buddydev_user_has_uploaded_cover( $user_id ) ){
		return $enabled;
	}
	return false;
	//now, we need to check if the user has uploade image or not
}

// a superbad hack since BuddyPress does not provide any specific hook
function buddydev_enable_cover_hook() {
	add_filter( 'bp_is_profile_cover_image_active', 'buddydev_check_for_uploaded_cover' );
}
add_action( 'bp_before_member_home_content', 'buddydev_enable_cover_hook' );

//disable it to avoid any sideecct on menus
//and we remove it immediately after header is loaded
function buddydev_disable_cover_hook() {
	if( has_filter( 'bp_is_profile_cover_image_active', 'buddydev_check_for_uploaded_cover' ) ) {
		remove_filter( 'bp_is_profile_cover_image_active', 'buddydev_check_for_uploaded_cover' );
	}
}
add_action( 'bp_before_member_header', 'buddydev_disable_cover_hook' );

This works with template pack and will work with any theme.

I personally don’t recommend this approach as it is very hakish. The reason we do it like above is BuddyPress template pack or BuddyPress is not giving us a separate function/hook to disable loading the cover-header template only. It uses same function everywhere, If we do filter on it everywhere, a user will not be able to see the upload cover photo link.

The better approach is to use only one function from my above code

/**
 * Check if user has uploaded cover
 * 
 * @param type $user_id
 * @return boolean
 */
function buddydev_user_has_uploaded_cover( $user_id ) {
	
	$cover_image = bp_attachments_get_attachment( 'url', array(
			'object_dir' => 'members',
			'item_id'    => $user_id,
		) );
	
	if( ! empty( $cover_image ) ) {
		return true;
	}
	
	return false;
}

and then look in members/single/home.php for this line

		<?php
		/**
		 * If the cover image feature is enabled, use a specific header
		 */
		if ( bp_displayed_user_use_cover_image_header() ) :
			bp_get_template_part( 'members/single/cover-image-header' );
		else :
			bp_get_template_part( 'members/single/member-header' );
		endif;
		?>

and change that to

		<?php
		/**
		 * If the cover image feature is enabled, use a specific header
		 */
		if ( buddydev_user_has_uploaded_cover( bp_displayed_user_id() ) ) :
			bp_get_template_part( 'members/single/cover-image-header' );
		else :
			bp_get_template_part( 'members/single/member-header' );
		endif;
		?>

That is much more meaningful and clean solution.

Hope that helps.

Please do let me know how it goes with you.

Regards
Brajesh

Hi Tony,
Thank you. I am glad I could help 🙂
Will be certainly opening a ticket on BuddyPress trac in a day or 2 regrading the same as it will be very useful if there was simple way to do it.

Marking this topic as resolved now.

Thank you
Brajesh