You can.
From this example in Docs (4.2, 5.0):
$user->roles()->sync(array(1 => array('expires' => true)));
Hardcoded version for the first two rows:
$food = Food::find(1);
$food->allergies()->sync([1 => ['severity' => 3], 4 => ['severity' => 1]]);
Dynamically, with your arrays $allergy_ids and $severities in a compatible state (size and sort), you shall prepare your sync data before. Something like:
$sync_data = [];
for($i = 0; $i < count($allergy_ids); $i++))
$sync_data[$allergy_ids[$i]] = ['severity' => $severities[$i]];
$food->allergies()->sync($sync_data);