Yes, most of the campaign is asking for Jr. member to participate in their ICO promotion program, if you are qualified with their specified limits then surely you can apply for the signature campaign. You can look at the service bounty section where you can find many bounties campaign.
Most probably the ico bounty campaigns is accepting Jr. Member, but here with signature campaign under services of bitcoin forum it won't be. When there's a campaign that let's you join with that rank, I guess it was just rare one and the amount of btc was a cheap offer for a Jr. Member participants. Please avoid any mistakes and violations of the rules of bitcointalk specially the campaigns in services section, in order to avoid being tagged negative trust because that's the number one reason of not being accepted.