Can A Nameserver Be Specified In An A Record By Another Nameserver

1) I use DNSMadeEasy for a couple of my important domains so I can utilize their failover service.

2) I use my own nameservers for everyone else.

At my register (GoDaddy) I've added host entries to my domain (let's call it host.com) for ALL of my nameservers: DNSMadeEasy and mine. For example here are my host entries:

1) nsdme0.host.com = 55.55.55.55 (DNSMadeEasy)
2) nsdme1.host.com = 56.55.55.55 (DNSMadeEasy)
3) nsdme2.host.com = 57.55.55.55 (DNSMadeEasy)
4) nsdme3.host.com = 58.55.55.55 (DNSMadeEasy)
5) nsdme4.host.com = 59.55.55.55 (DNSMadeEasy)
6) ns1.host.com = 60.55.55.55 (mine)
7) ns2.host.com = 61.55.55.55 (mine)

At the register I've then configured host.com to use the first five nameservers for itself, the DNSMadeEasy nameservers.

For less critical sites that I host I simply point them to ns1.host.com and ns2.host.com, my nameservers.

Now, here's the twist. If I use dig to look up www.host.com I get:

[root@lax1 ~]# dig +trace www.host.com

; <<>> DiG 9.3.3rc2 <<>> +trace www.host.com
;; global options: printcmd
. 220048 IN NS D.ROOT-SERVERS.NET.
...........................................
. 220048 IN NS K.ROOT-SERVERS.NET.
;; Received 228 bytes from 66.63.160.2#53(66.63.160.2) in 1 ms

net. 172800 IN NS J.GTLD-SERVERS.net.
...........................................
net. 172800 IN NS G.GTLD-SERVERS.net.
;; Received 497 bytes from 128.8.10.90#53(D.ROOT-SERVERS.NET) in 74 ms

host.com. 172800 IN NS nsdme0.host.com.
host.com. 172800 IN NS nsdme1.host.com.
host.com. 172800 IN NS nsdme2.host.com.
host.com. 172800 IN NS nsdme3.host.com.
host.com. 172800 IN NS nsdme4.host.com.
;; Received 225 bytes from 192.48.79.30#53(J.GTLD-SERVERS.net) in 125 ms

www.host.com. 1800 IN CNAME host.com.
host.com. 75 IN A 60.55.55.55
host.com. 86400 IN NS nsdme2.host.com.
host.com. 86400 IN NS nsdme1.host.com.
host.com. 86400 IN NS nsdme5.host.com.
host.com. 86400 IN NS nsdme0.host.com.
host.com. 86400 IN NS nsdme4.host.com.
host.com. 86400 IN NS nsdme3.host.com.
;; Received 276 bytes from 123.123.123.123#53(nsdme0.host.com) in 68 ms
BUT, if I lookup the nameserver (ns1.host.com) I get:

Code:
[root@lax1 ~]# dig +trace ns1.host.com

; <<>> DiG 9.3.3rc2 <<>> +trace ns1.host.com
;; global options: printcmd
. 218964 IN NS M.ROOT-SERVERS.NET.
...........................................
. 218964 IN NS K.ROOT-SERVERS.NET.
;; Received 228 bytes from 66.63.160.2#53(66.63.160.2) in 1 ms

net. 172800 IN NS H.GTLD-SERVERS.net.
...........................................
net. 172800 IN NS G.GTLD-SERVERS.net.
;; Received 497 bytes from 202.12.27.33#53(M.ROOT-SERVERS.NET) in 115 ms

ns1.host.com. 172800 IN A 60.55.55.55
host.com. 172800 IN NS nsdme0.host.com.
host.com. 172800 IN NS nsdme1.host.com.
host.com. 172800 IN NS nsdme2.host.com.
host.com. 172800 IN NS nsdme3.host.com.
host.com. 172800 IN NS nsdme4.host.com.
;; Received 241 bytes from 192.54.112.30#53(H.GTLD-SERVERS.net) in 151 ms

What I've realized is that the actual IP addresses for nameserver host entries come from a higher level server than my own, in this case H.GTLD-SERVERS.net. I guess this makes sense but I just hadn't realized it before. It looks like I don't even need to have record entries in my DNS records for the host nameservers.

Now for the question. Can I:

1) Remove my custom host nameserver entries from my register.

2) Add entries in my DNSMadeEasy records to specify the location of ns1.host.com and ns2.host.com.

3) Use the failover provided by DNSMadeEasy to also fail-over my DNS entries for my nameservers?

I know this would require one more hop if it works but it would allow me to provide failover ability to fifty domains without having to purchase the extra domains at DNSMadeEasy.